White Mountains Insurance SC TOI Issuer tender offer statement | WTM 24 Feb 12

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Exhibit (a)(1)(H)

LETTER TO PARTICIPANTS IN THE
ONEBEACON 401(K) SAVINGS AND EMPLOYEE STOCK OWNERSHIP PLAN

February 24, 2012

Dear Plan Participant:

White Mountains Insurance Group, Ltd., a company organized under the laws of Bermuda (the "Company"), is offering to purchase up to 1,000,000 of its Common Shares, par value $1.00 per share (the "Shares"), at a purchase price of $500 per Share (the "Purchase Price"), net to the seller in cash, less any applicable withholding taxes and without interest, upon the terms and subject to the conditions set forth in the Offer to Purchase (as it may be amended or supplemented from time to time, the "Offer to Purchase") and in the related Letter of Transmittal (the "Letter of Transmittal" and, together with the Offer to Purchase, as they may be amended or supplemented from time to time, the "Offer"), including the proration provisions described therein. Because of the proration and "odd lot" priority provisions described in this Offer to Purchase, fewer than all of the Shares tendered may be purchased if more than the number of Shares the Company seeks are properly tendered. Shares tendered but not purchased in the Offer will be returned to the tendering shareholders at the Company's expense promptly after the expiration of the Offer.

A copy of each of the Offer to Purchase, the 401(k) Plan Participant Q&A, the 401(k) Plan Participant Election Form (the "Election Form") and the 401(k) Plan Participant Notice of Withdrawal (the "Notice of Withdrawal") is enclosed with this letter. You are urged to examine these documents and the Offer carefully.

As a participant in the OneBeacon 401(k) Savings and Employee Stock Ownership Plan (the "Plan"), you have the right to instruct Vanguard Fiduciary Trust Company, the Trustee of the Plan (the "Trustee") via communication with Computershare Trust Company, N.A., as agent (the "Agent") for the benefit of the Trustee, as to whether to tender any Shares allocated to your Plan account ("Plan Shares"). If, after reading the enclosed materials, you want to tender your Plan Shares, you must follow the instructions contained in this letter and fill out and sign the Election Form enclosed, and mail the form in the enclosed postage-paid pre-addressed envelope to the Agent in connection with the Offer. If you do not wish to use the enclosed envelope, you may also send your Election Form by (i) facsimile to (866) 263-8381, which is highly encouraged, or (ii) express or overnight delivery to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, 250 Royall Street, Suite V, Canton, Massachusetts 02021, or by first-class, registered or certified mail to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, PO Box 43011, Providence, Rhode Island 02940-3011.

If valid instructions to tender Plan Shares are not received by 5:00 p.m., New York City time, on March 16, 2012, the Plan Shares allocated to your Plan account will not be tendered unless the Company extends the Offer, in which case your instructions must be received by 5:00 p.m., New York City time, on the date that is four (4) business days before the new expiration date.Please note that your instructions as to whether or not to tender will be kept confidential from the Company and OneBeacon Insurance Company (the "Plan Sponsor").

To ensure that your Election Form is received in a timely manner, you are strongly encouraged to send it by facsimile to the Agent at (866) 263-8381. This fax number is only valid for Plan Shares. If you hold Shares outside of the Plan and attempt to tender the Shares held outside of the Plan through this facsimile number, those tender instructions will not be valid.

If you elect to tender Plan Shares and such Plan Shares are accepted in the Offer, any proceeds received in respect of such Plan Shares will remain in the Plan. If investment instructions directing the investment of any tender proceeds are not received prior to the receipt of the proceeds by the Plan, any proceeds received with respect to such shares will be invested in the Plan's Qualified Default Investment Alternative ("QDIA"), which is the Vanguard Target Retirement Fund closest to the year you will turn age 65. However, you may elect to redirect the proceeds to any other investment fund

under the Plan that is open for new investments at any time once the proceeds have been allocated to your account under the Plan.

Whether you decide to tender your Plan Shares or not, all Plan Shares in the White Mountains ESOP Fund (the "ESOP Fund") in the Plan will be "frozen" for two business days. Transactions involving the ESOP Fund in the Plan will not be permitted starting at 1:00 p.m. Eastern time on Tuesday, March 20, 2012, unless the Offer is extended or withdrawn prior to that time. If the Offer is extended, the ESOP Fund will be "frozen" starting at 1:00 p.m. Eastern time on the date that is two business days before any new expiration date.

If you choose to instruct the Trustee to tender your Plan Shares, certain transactions involving the Plan, including all withdrawals, distributions and transfers, will be prohibited until the earlier of such time as: (i) the Offer is terminated and all Plan Shares are returned to the Trustee or (ii) the Offer is consummated and the Plan Shares are purchased by the Company. These restrictions on transactions will apply only to Plan Shares tendered into the Offer and will not apply to any Plan Shares not tendered into the Offer. In the event that the Offer is extended, the restrictions on transactions involving the Plan will continue until the consummation or expiration of the Offer, as extended.

You must direct the Trustee if you want to tender your Plan Shares. The Trustee will tender your Plan Shares only if specifically instructed to do so.

If you do not respond using the enclosed Election Form, you will be deemed to have instructed the Trustee not to tender any of your Plan Shares under the Offer, and your Plan Shares will remain in your Plan account.

If you are also a direct shareholder of the Company, you will receive under separate cover another copy (or copies) of the Offer documents which can be used to tender your directly held Shares if you choose to do so. Instructions with respect to tendering your directly held Shares will be set forth in those materials. Those Offer documents may not be used to direct the Trustee to tender or not to tender the Plan Shares allocable to your individual account under the Plan.

Please note that the Plan is prohibited by law from selling Plan Shares to the Company for a price that is less than the prevailing market price of the Company's common stock. If the closing price of the Company's common stock on the date the Offer expires is greater than the price available in the Offer, none of the Plan Shares will be tendered and your tender instruction will be deemed to have been withdrawn.

You also may request that the Trustee withdraw any tender instruction you have previously submitted, as long as you do so prior to 5:00 p.m., New York City time, on March 16, 2012, by delivering the Notice of Withdrawal to the Agent. The Notice of Withdrawal cannot be sent by facsimile. Any Notice of Withdrawal that is sent by facsimile to the Agent will not be considered valid. If you do not have a copy of the Notice of Withdrawal, you may also give your withdrawal instructions (which must contain the information set forth below) by letter to the Agent. If the Offer is extended and you wish to withdraw your previously submitted tender instruction, then you must ensure that the Agent receives your Notice of Withdrawal or other withdrawal notice by 5:00 p.m., New York City time, on the date that is four (4) business days before the new expiration date. The Notice of Withdrawal sent to the Agent must: (i) specify the name of the participant or beneficiary who has made the instruction that is being withdrawn and the participant's or beneficiary's social security number and (ii) be signed by the participant or beneficiary who signed the Election Form.

If you wish to withdraw any tender instructions for Plan Shares, you must withdraw the tender instructions for all Plan Shares that have been submitted into the Offer. You may instruct the Trustee to re-tender any or all of these Plan Shares into the Offer by submitting a new Election Form by mail or facsimile.

For any Plan Shares that are tendered and purchased by the Company, the Company will pay cash to the Plan.Individual participants in the Plan will not, however, receive any cash tender proceeds directly. All such proceeds will remain in the Plan and may be withdrawn only in accordance with the terms of the Plan.

None of the Trustee, the Agent, the Company, the Plan Sponsor, the Company's Board of Directors, Computershare Trust Company, N.A., which is acting as the depositary (in such capacity, the "Depositary") or D.F. King & Co., Inc., which is acting as the information agent (the "Information Agent"), makes any recommendation as to whether you should tender or refrain from tendering your Plan Shares. You must make your own decision as to whether to tender your Plan Shares and, if so, how many Plan Shares to tender.

If you have any questions about the Offer, you should contact D.F. King & Co., Inc., the Information Agent for the Offer, toll-free, at (800) 967-4607 or, collect, at (212) 269-5550. Additionally, all tender offer materials are available online at www.sec.gov. If you have questions about your Plan account or questions about how to provide tender instructions to Vanguard, please contact Vanguard Participant Services at (800) 523-1188 Monday through Friday from 8:30 a.m. to 9 p.m., Eastern time.

Vanguard Fiduciary Trust Company

QUESTIONS AND ANSWERS WTM RESPECT TO
TENDER RIGHTS OF PARTICIPANTS IN
THE ONEBEACON 401(K) SAVINGS AND EMPLOYEE STOCK OWNERSHIP PLAN

DESCRIPTION OF THE OFFER

1. What is the Offer?

Participants in the OneBeacon 401(k) Savings and Employee Stock Ownership Plan (the "Plan") who have equivalent Shares allocated to their Plan accounts (such Shares are referred to in this Q&A as "Plan Shares") may tender these Plan Shares by filling out and signing the Election Form enclosed, and mailing the form in the enclosed postage-paid pre-addressed envelope to Computershare Trust Company, N.A., as agent (the "Agent") for the benefit of Vanguard Fiduciary Trust Company (the "Trustee"). If you do not wish to use the enclosed envelope, you may also send your Election Form by (i) facsimile to (866) 263-8381 or (ii) express or overnight delivery to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, 250 Royall Street, Suite V, Canton, Massachusetts 02021, or by first-class, registered or certified mail to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, PO Box 43011, Providence, Rhode Island 02940-3011.

You should mail or facsimile your completed Election Form to the Agent no later than 5:00 p.m., New York City time, on March 16, 2012, or, if the Offer is extended, by 5:00 p.m., New York City time, on the date that is four (4) business days before the new expiration date. To ensure that your Election Form is received in a timely manner, you are strongly encouraged to send it by facsimile to the Agent at (866) 263-8381.

In the event that more than 1,000,000 Shares are tendered in the Offer, the Company may exercise its right to increase the number of Shares sought in the Offer by an amount not exceeding 2% of our outstanding Shares without extending the expiration date. The Company also expressly reserves the right, in its sole discretion, to purchase additional Shares, subject to applicable law.

If more than 1,000,000 Shares (or such greater number of Shares as we may elect to purchase, subject to applicable law) are properly tendered and not properly withdrawn, the Company will purchase Shares in the following order of priority:

•: First, the Company will purchase all "odd lots" of less than 100 Shares from shareholders who properly tender all of their Shares and who do not properly withdraw them before the expiration date; and
•: Second, after purchasing all the "odd lots" that were properly tendered, the Company will purchase Shares from all other holders who properly tender Shares and who do not properly

withdraw them before the expiration date, on a pro rata basis, with appropriate adjustments to avoid purchases of fractional Shares, until we have acquired the number of Shares that we have offered to purchase.

Therefore, the Company may not purchase all the Shares that you tender.

The terms and conditions of the Offer are fully described in the enclosed Offer to Purchase. Please read the Offer to purchase carefully.

2. What are my rights under the Offer?

The Plan records indicate that Plan Shares are allocated to your account. You may tender some or all of these Shares. Because the Employee Retirement Income Security Act of 1974, as amended ("ERISA"), requires that all Plan assets in most circumstances be held in trust, all of these Plan Shares are registered in the name of Vanguard Fiduciary Trust Company. Consequently, the Trustee will actually tender your Plan Shares by aggregating all Plan participant instructions and completing the required letter of transmittal for all Plan participants, but only in accordance with your instructions as well as those of the other Plan participants.

You must direct the Trustee if you want to tender your Plan Shares. The Trustee will tender your Plan Shares only if specifically instructed to do so. If you do not respond using the enclosed Election Form, you will be deemed to have instructed the Trustee not to tender any of your Plan Shares under the Offer, and your Plan Shares will remain in your Plan account.

The Agent is acting on behalf of the Trustee in connection with the Offer.

Plan Shares will not qualify for the "odd lot" preference described above and may not be conditionally tendered. See Section 1 of the Offer to Purchase for a description of the "odd lot" preference.

3. Which documents did I receive in the Offer materials and what is the purpose of each document?

The following materials are enclosed in this mailing:

(a): Letter from the Trustee. This letter gives you details for participating in the Offer with respect to the Plan Shares in your Plan account.
(b): Offer to Purchase dated February 24, 2012. This document describes all of the terms and conditions of the Offer.Please read this document carefully.
(c): Election Form.You must complete, sign and mail this document to the Agent if you wish to direct the Trustee to tender some or all of your Plan Shares. If your fully completed Election Form is not received by the Agent by 5:00 p.m., New York City time, on March 16, 2012, you will be deemed to have instructed the Trustee not to offer any of your Plan Shares for sale under the Offer. You must use the Election Form if you wish to direct a tender of your Plan Shares.
(d): Reply Envelope. A postage-paid pre-addressed envelope is provided for your convenience. If you decide to tender some or all of your Plan Shares, you may use this envelope to mail the completed Election Form to the Agent, or facsimile instructions.
(e): Notice of Withdrawal. This form can be used to withdraw Plan Shares tendered into the Offer. See Q&A #11 below for additional information.

4. How do I direct the Plan Trustee?

The only way to instruct the Trustee to tender your Plan Shares is by completing the Election Form as described, signing it and returning it to the Agent.

If you choose to mail your Election Form to the Agent, you may do this by using the postage-paid pre-addressed envelope provided for this purpose. Alternatively, you may send your Election Form by (i) facsimile to (866) 263-8381 or (ii) first-class, registered or certified mail or express or overnight delivery to the Agent.

The Agent must receive your Election Form before 5:00 p.m., New York City time, on March 16, 2012 (unless the Offer is extended, in which case such Election Form must be received by no later than 5:00 p.m., New York City time, on the date that is four (4) business days before the new expiration date). If you send the Agent the Election Form, you must sign and complete the Election Form for your tender instruction to be valid.

To validly direct the Trustee to Tender Plan Shares on your behalf by mailing the Election Form, you must:

(a): Instructions. Read carefully and follow exactly the instructions in (i) the Letter from the Trustee and (ii) the Election Form. These documents will tell you how to direct the Trustee regarding your Plan Shares.
(b): Election Form. Complete the enclosed Election Form.
(c): Shares. Designate on the Election Form the percentage of your Plan Shares you wish to be tendered.
(d): Signature. You must SIGN the Election Form to complete your instruction. Unless you sign the Election Form, your direction cannot be honored, and the Election Form will be ineffective even if it is timely received by the Trustee.
(e): Facsimile. You are highly encouraged to send your Election Form to the Agent by facsimile transmission to (866) 263-8381.
(f): Mailing. We have enclosed a postage-paid pre-addressed return envelope with your tender materials. You may use this postage-paid pre-addressed envelope to return your completed Election Form if you wish to have the Trustee tender your Plan Shares. If you do not wish to use the enclosed envelope, you may also send your Election Form by first-class, registered or certified mail to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, PO Box 43011, Providence, Rhode Island 02940-3011, or by express or overnight delivery to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, 250 Royall Street, Suite V, Canton, Massachusetts 02021.

Please be precise in providing your instruction and please act promptly.Do not deliver your instructions to your Human Resources Department or The Vanguard Group, Inc. ("Vanguard").

If you do not wish to tender any Plan Shares, take no action.

5. Must I provide directions to the Trustee?

You must respond to the Agent only if you wish the Trustee to tender any of your Plan Shares.If you do not wish to tender any of your Plan Shares, do nothing. If you do nothing, you will be deemed to have instructed the Trustee not to tender any of the Plan Shares held for your benefit. A failure to respond to this tender offer will be deemed as an instruction not to tender your Plan Shares.

6. How many Plan Shares may I tender and how do I learn the number of Plan Shares held for my benefit in the Plan?

You may tender a whole percentage (up to 100%) of the Plan Shares allocated to your Plan account as of the expiration date of the Offer, currently scheduled to occur on March 22, 2012 (unless it is extended). The approximate number of Plan Shares held in your Plan account is calculated by dividing the value of your Plan account allocated to the White Mountains ESOP Fund under the Plan by the New York Stock Exchange closing price of the Company's common shares on a particular day. You may obtain information about the number of Plan Shares allocated to your Plan account, or confirm your current balance, by contacting Vanguard at (800) 523-1188 or www.vanguard.com for assistance.

7. Why must I direct the tender of Plan Shares allocated to my Plan account by whole percentage, rather than designating a set number of Plan Shares?

A whole percentage designation allows the Trustee to take into account transactions involving Plan Shares that might be effected after you complete and send your Election Form to the Agent, such as additional contributions to investment funds under the Plan that are open for new investments, exchanges or distributions of Plan Shares. The percentage designation allows the Trustee to tender your Plan Shares based on the actual number of Shares in your Plan account as of the date of such tender.

8. What if I have Shares in my Plan account and hold Shares outside of the Plan?

If you have Shares in the Plan and also own other Shares (either in your possession or held by a bank or brokerage firm, or otherwise) outside of the Plan, you will receive two or more sets of Offer materials. You should be careful to follow the different instructions that apply to tendering each kind of Shares.

9. Who will know whether I tendered my Plan Shares?

Your directions to the Agent for the benefit of the Trustee will be kept confidential. No employee, officer or director of the Company will learn of your instruction unless such disclosure is required by law.

10. Can I change my mind and direct the Trustee to withdraw Plan Shares that I previously directed the Trustee to tender?

Yes, but only if you perform all of the following steps:

(a): You must send a completed and signed copy of the enclosed Notice of Withdrawal or other withdrawal notice to the Agent. You may submit a Notice of Withdrawal or other withdrawal notification by first-class, registered or certified mail to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, PO Box 43011, Providence, Rhode Island 02940-3011, or by express or overnight delivery to the Agent at Computershare Trust Company, N.A., c/o Voluntary Corporate Actions, 250 Royall Street, Suite V, Canton, Massachusetts 02021;
(b): The Notice of Withdrawal cannot be sent by facsimile. Any Notice of Withdrawal that is sent by facsimile to the Agent will not be considered valid;
(c): The Notice of Withdrawal or other withdrawal notice must set forth your name and social security number and it must state that you are directing the Trustee to withdraw all Plan Shares that you previously directed the Trustee to tender on your behalf; and

(d): The Agent must receive the Notice of Withdrawal or other withdrawal notice before 5:00 p.m., New York City time, on March 16, 2012 (unless the Offer is extended, in which case such notice must be received by no later than 5:00 p.m., New York City time, on the date that is four (4) business days before the new expiration date).

If you wish to withdraw any tender instructions for Plan Shares with respect to the Offer, you must withdraw the tender instructions for all Plan Shares that have been submitted into the Offer. You may instruct the Trustee to re-tender any or all of these Plan Shares into the Offer by submitting a new Election Form by mail or facsimile to the Agent.

11. Will the Company purchase all Plan Shares that I direct the Trustee to tender?

The answer to this question depends on the total number of Shares validly tendered (and not validly withdrawn) by all tendering shareholders. If more than 1,000,000 Shares (or such greater number of Shares as the Company may elect to purchase, subject to applicable law) are properly tendered, then the Company will purchase your Plan Shares subject to the proration provisions of the Offer. See Q&A #1 for a description of how the proration process works.

Please note that the Plan is prohibited by law from selling Plan Shares to the Company for a price that is less than the prevailing market price of the Company's Shares. If the closing price of the Company's shares on the date the Offer expires is greater than the price available in the Offer, none of the Plan Shares will be tendered and your tender will be deemed to have been withdrawn.

Plan Shares held in your Plan account that are tendered but not purchased by the Company will remain in your Plan account as if nothing had happened, subject to the rules and provisions governing the Plan.

12. What if I have questions about the Offer relating to the Plan?

If you have any questions about the Offer, please contact D.F. King & Co., the Information Agent for the Offer, at (800) 967-4607 (toll free) or, collect at (212) 269-5550. Additionally, all tender offer materials are available online at www.sec.gov. If you have questions about your Plan account or questions about how to provide tender instructions to Vanguard, please contact Vanguard Participant Services at (800) 523-1188 Monday through Friday from 8:30 a.m. to 9 p.m., Eastern time.

13. How will I know if the Company has purchased my Plan Shares?

The purchase will be reflected in your Plan account as a transfer of the tendered Plan Shares. The tender proceeds will not be in your account until six (6) to ten (10) business days after the Offer expires. At that time, you will be able to see the proceeds in your account on www.vanguard.com, and they will be reflected on your next quarterly statement.

OPERATION OF THE PLAN DURING THE OFFER

14. What happens to contributions to my Plan account that are made after March 16, 2012?

Contributions made to your Plan account after March 16, 2012 will be allocated as usual, in accordance with the sources of the contributions and, where applicable, your investment directions in effect at the time of your contribution, including any direction to invest such contributions in Plan Shares. Contributions will continue to be allocated during the Offer, and all of the Plan Shares in your Plan account on March 22, 2012 at 5:00 p.m., New York City time, will be subject to the Offer, unless the Offer is extended, in which case only the Plan Shares in your Plan account at 5:00 p.m., New York City time, on the expiration date will be subject to the Offer.

15. How will my Plan account be affected by the Offer?

You will be temporarily unable to conduct certain Plan transactions involving Plan Shares in your Plan account prior to the expiration of Offer. Please review the Plan Letter for more information.

16. What happens if I request a distribution, withdrawal or transfer following the announcement of the Offer, but before I instruct the Trustee to tender my Plan Shares?

Distributions and withdrawals from the Plan and transfers into or out of your Plan account will be processed in accordance with normal procedures except for Plan Shares that you have instructed the Trustee to tender into the Offer. In addition, as explained in the Plan Letter, all Plan Shares will be temporarily frozen two business days prior to the expiration date of the Offer.

17. Will I be taxed on any proceeds received in 2012 from the Shares that I tender from my Plan account?

No. Because tender proceeds received from Plan Shares will be received by and held in your Plan, they will not be subject to current income taxes.

REINVESTMENT OF OFFER PROCEEDS

18. How will the Plan invest the proceeds received from the Plan Shares that are tendered?

If investment instructions directing the investment of any tender proceeds are not received prior to the receipt of the proceeds by the Plan, any proceeds received with respect to such shares will be invested in the Plan's Qualified Default Investment Arrangement ("QDIA"), which is the Vanguard Target Retirement Fund closest to the year you will turn age 65. Once the proceeds are in your Plan account, you will be able to move such tender proceeds at your own discretion to other investment funds of your choosing within the Plan.

ELECTION FORM
OneBeacon 401(k) Savings and Employee Stock Ownership Plan (the "Plan")
Your election must be received no later than 5:00 p.m.,
New York City time, on March 16, 2012,
to be included in the tabulation, unless the Offer is extended.

In accordance with the White Mountains Insurance Group, Ltd. (the "Company") Offer to Purchase dated February 24, 2012 (the "Offer to Purchase"), a copy of which I have received, I hereby instruct Vanguard Fiduciary Trust Company (the "Trustee") to tender or not to tender shares of the Company, par value $1.00 per share (the "Shares"), allocated to my Plan account ("Plan Shares") prior to the Expiration Date (as defined in the Offer to Purchase), as follows:

1.: If you do NOT want to tender any of the shares of White Mountains common stock allocated to your account in the Plan, do NOT return this form. If you do nothing, none of your shares will be tendered, unless otherwise required by law or the terms of the Plan.
2.: By writing a whole percentage of Plan Shares allocated to my Plan account in the space below, I elect to tender such percentage of Plan Shares allocated to my Plan account as of the expiration date of the Offer.


		%

VOLUNTARY CORPORATE ACTION COY: WTM VANGAURD 401(k) PLAN

You must direct the Trustee if you want to tender your Plan Shares. The Trustee will tender your Plan Shares only if the Trustee is specifically instructed to do so.

If you do not submit this Election Form to the Agent, who is acting on behalf of the Trustee in connection with the Offer, you will be deemed to have instructed the Trustee not to tender any of your Plan Shares under the Offer, and your Plan Shares will remain in your Plan account.

If you submit more than one Election Form, the Trustee will rely on the last instructions received from you. The later set of instructions will revoke all prior instructions given to the Trustee with respect to this Offer. Please see the letter from Vanguard Fiduciary Trust Company to participants in the OneBeacon 401(k) Savings and Employee Stock Ownership Plan, dated February 24, 2012 (the "Plan Letter") for additional information on revoking previously submitted instructions.

Because you are designated a "named fiduciary" for tender offer purposes under your Plan account, the Trustee is required to follow your validly delivered instructions, provided they are in accordance with the terms of the Plan and are not inconsistent with the Trustee's responsibilities under the Employee Retirement Income Security Act of 1974, as amended ("ERISA"). By signing, dating and returning this instruction form, you accept this designation under the Plan as a "named fiduciary", and that the adjustment to your instructions described below may be made by the Trustee.

The Plan is prohibited by law from selling your Plan Shares (as defined in the Plan Letter) to the Company for a price that is less than the prevailing market price of the Shares. If the closing price of the Company's common stock on the date the Offer expires is greater than the price available in the Offer, none of the Plan Shares will be tendered pursuant to your tender instruction above and your instruction will be deemed to have been withdrawn.


X

Signature


Print Name


Dated:
		Incorrectly completed or unsigned forms will be discarded in the Offer.


Phone Number:
		To be used in the event the Agent needs to contact you regarding your Election.

[LABEL WITH PARTICIPANT'S
NAME AND ADDRESS]

VOLUNTARY CORPORATE ACTION COY: WTM VANGUARD 401k PLAN

NOTICE OF WITHDRAWAL FROM THE TENDER OFFER

WHITE MOUNTAINS INSURANCE GROUP, LTD. TENDER OFFER
FOR PARTICIPANTS IN ONEBEACON 401(K) SAVINGS AND EMPLOYEE
STOCK OWNERSHIP PLAN

To: Computershare Trust Company, N.A., as Agent:

As a participant in the above-referenced Plan, I hereby instruct Vanguard Fiduciary Trust Company, the trustee (the "Trustee") of the OneBeacon 401(k) Savings and Employee Stock Ownership Plan, which holds the common shares of White Mountains Insurance Group, Ltd., to withdraw from the Offer (as defined in the Offer to Purchase) all Plan Shares (as defined in the Letter from Vanguard Fiduciary Trust Company to Participants in the OneBeacon 401(k) Savings and Employee Stock Ownership Plan, dated February 24, 2012 (the "Plan Letter")) that I previously instructed the Trustee to tender on my behalf, pursuant to the Offer (as defined in the Letter).


Signature		Date
Please print name clearly		Social Security Number


Address:
				Daytime Phone Number

DO NOT USE THIS FORM TO TENDER YOUR PLAN SHARES.
ONLY USE THIS FORM TO WITHDRAW YOUR PREVIOUS TENDER OF PLAN SHARES
FROM THE OFFER.

Mail this withdrawal notice promptly to:


By First-Class, Registered or Certified Mail:		By Express or Overnight Delivery:
Computershare Trust Company, N.A., Depositary c/o Voluntary Corporate Actions PO Box 43011 Providence, Rhode Island 02940-3011		Computershare Trust Company, N.A., Depositary c/o Voluntary Corporate Actions 250 Royall Street, Suite V Canton, Massachusetts 02021

QuickLinks

Exhibit (a)(1)(H)

White Mountains Insurance (WTM) SC TO-IIssuer tender offer statement