
<PAGE>   1
 
                                                                  EXHIBIT (a)(4)
 
                           OFFER TO PURCHASE FOR CASH
                     ALL OUTSTANDING SHARES OF COMMON STOCK
            (INCLUDING THE ASSOCIATED COMMON SHARE PURCHASE RIGHTS)
 
                                       OF
 
                 AMERIWOOD INDUSTRIES INTERNATIONAL CORPORATION
 
                                       BY
 
                           HORIZON ACQUISITION, INC.
                      AN INDIRECT WHOLLY-OWNED SUBSIDIARY
 
                                       OF
 
                             DOREL INDUSTRIES INC.
 
                                       AT
 
                              $9.625 NET PER SHARE
 
THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY
TIME, ON THURSDAY, APRIL 30, 1998, UNLESS THE OFFER IS EXTENDED.
 
To Brokers, Dealers, Banks, Trust                                  April 3, 1998
  Companies and Other Nominees:
 
     We have been engaged by Horizon Acquisition, Inc., a Delaware corporation
(the "Purchaser"), which is an indirect wholly-owned subsidiary of Dorel
Industries Inc., a Quebec, Canada corporation ("Parent"), to act as the
Information Agent in connection with the Purchaser's offer to purchase all
outstanding shares of Common Stock, $1.00 par value per share (the "Common
Stock"), including the associated common share purchase rights (the "Rights,"
and together with the Common Stock, the "Shares"), of Ameriwood Industries
International Corporation, a Michigan corporation (the "Company"), at $9.625 per
Share, net to the seller in cash, without interest thereon, upon the terms and
subject to the conditions set forth in the Purchaser's Offer to Purchase dated
April 3, 1998 (the "Offer to Purchase") and in the related Letter of Transmittal
(which, together with any amendments or supplements thereto, collectively
constitute the "Offer"). Please furnish copies of the enclosed materials to
those of your clients for whom you hold Shares registered in your name or in the
name of your nominee.
 
     Enclosed herewith are copies of the following documents:
 
     1.  Offer to Purchase dated April 3, 1998;
 
     2.  Letter of Transmittal to be used by shareholders of the Company in
         accepting the Offer;
 
     3.  A printed form of letter that may be sent to your clients for whose
         account you hold Shares in your name or in the name of a nominee, with
         space provided for obtaining such clients' instructions with regard to
         the Offer;
 
     4.  Notice of Guaranteed Delivery; and
 
     5.  Guidelines for Certification of Taxpayer Identification Number on
         Substitute Form W-9.
 
     The Offer is conditioned upon, among other things, there having been
validly tendered and not withdrawn prior to the Expiration Date (as defined in
the Offer to Purchase) that number of Shares which, when added to any Shares
already owned by the Purchaser and Parent, represents at least a majority of all
outstanding Shares on a fully diluted basis on the date of purchase.
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     Upon the terms and subject to the conditions of the Offer (including, if
the Offer is extended or amended, the terms and conditions of any such extension
or amendment), the Purchaser will accept for payment and will pay promptly after
the Expiration Date (as defined in the Offer to Purchase) for all shares validly
tendered prior to the Expiration Date and not properly withdrawn as, if and when
the Purchaser gives oral or written notice to the Depositary of the Purchaser's
acceptance of such Shares. Payment for Shares accepted for payment pursuant to
the Offer will be made only after timely receipt by the Depositary of (i)
certificates for such Shares (or a timely Book-Entry Confirmation (as defined in
the Offer to Purchase) with respect thereto), (ii) a Letter of Transmittal (or
facsimile thereof), properly completed and duly executed, with any required
signature guarantees, or, in the case of a book-entry transfer, an Agent's
Message (as defined in the Offer to Purchase), and (iii) any other documents
required by the Letter of Transmittal.
 
     If holders of Shares wish to tender their Shares, but it is impracticable
for them to deliver their certificates on or prior to the Expiration Date or to
comply with the book-entry transfer procedures on a timely basis, a tender may
be effected by following the guaranteed delivery procedures specified in Section
2 of the Offer to Purchase.
 
     YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS
PROMPTLY. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00
MIDNIGHT, NEW YORK CITY TIME, ON THURSDAY, APRIL 30, 1998, UNLESS EXTENDED.
 
     Neither the Purchaser nor Parent will pay any fees or commissions to any
broker or dealer or other person (other than the Information Agent as described
in the Offer to Purchase) in connection with the solicitation of tenders of
Shares pursuant to the Offer. The Purchaser will, however, upon request,
reimburse brokers, dealers, commercial banks and trust companies for reasonable
and necessary costs and expenses incurred by them in forwarding materials to
their customers. The Purchaser will pay all stock transfer taxes applicable to
its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the
Letter of Transmittal.
 
     Additional copies of the enclosed materials may be obtained by contacting
the Information Agent at its address and telephone numbers set forth on the back
cover of the enclosed Offer to Purchase.
 
                                          Very truly yours,
 
                                          Innisfree M&A Incorporated
                                          501 Madison Avenue,
                                          20th Floor
                                          New York, New York 10022
                                          Telephone: (212) 750-5833
                                                 or
                                          Call Toll Free (888) 750-5834
 
     NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU OR
ANY OTHER PERSON THE AGENT OF THE PURCHASER, PARENT, THE DEPOSITARY, THE
INFORMATION AGENT OR AUTHORIZE YOU OR ANY OTHER PERSON TO GIVE ANY INFORMATION
OR MAKE ANY REPRESENTATION ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFER
NOT CONTAINED IN THE OFFER TO PURCHASE OR THE LETTER OF TRANSMITTAL.
