
<PAGE>   1
 
                                                                  EXHIBIT (a)(3)
 
                         NOTICE OF GUARANTEED DELIVERY
 
                                      FOR
 
                        TENDER OF SHARES OF COMMON STOCK
            (INCLUDING THE ASSOCIATED COMMON SHARE PURCHASE RIGHTS)
 
                                       OF
 
                 AMERIWOOD INDUSTRIES INTERNATIONAL CORPORATION
 
     As set forth in Section 2 of the Offer to Purchase (as defined below), this
form or one substantially equivalent hereto must be used to accept the Offer (as
defined below) if certificates for 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"), are not immediately available, or if the procedure for book-entry
transfer cannot be completed on a timely basis or time will not permit all
required documents to reach the Depositary at the address set forth below prior
to the Expiration Date (as defined in the Offer to Purchase). This form may be
delivered by hand to the Depositary or transmitted by telegram, facsimile
transmission or mail to the Depositary and must include a guarantee by an
Eligible Institution (as defined in the Offer to Purchase). See Section 2 of the
Offer to Purchase.
 
                        The Depositary for the Offer is:
 
                        HARRIS TRUST COMPANY OF NEW YORK
 
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<S>                                            <C>
                   By Mail:                             By Hand/Overnight Delivery:
             Wall Street Station                               Receive Window
                P.O. Box 1023                                Wall Street Plaza
           New York, NY 10268-1023                       88 Pine Street, 19th Floor
                                                             New York, NY 10005
                                 By Facsimile Transmission:
                                       (212) 701-7636
                                 For Information Telephone:
                                       (212) 701-7624
</TABLE>
 
     DELIVERY OF THIS INSTRUMENT TO AN ADDRESS, OR TRANSMISSION OF INSTRUCTIONS
VIA A FACSIMILE NUMBER, OTHER THAN AS SET FORTH ABOVE DOES NOT CONSTITUTE A
VALID DELIVERY.
 
     This form is not to be used to guarantee signatures. If a signature on a
Letter of Transmittal is required to be guaranteed by an Eligible Institution
under the instructions thereto, such signature guarantee must appear in the
applicable space provided in the signature box on the Letter of Transmittal.
<PAGE>   2
 
Ladies and Gentlemen:
 
     The undersigned hereby tenders to Horizon Acquisition, Inc., a Delaware
corporation (the "Purchaser"), which is an indirect wholly-owned subsidiary of
Dorel Industries Inc., a Quebec, Canada corporation, 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 the related Letter of Transmittal, receipt
of which is hereby acknowledged, the number of Shares (as such term is defined
in the Offer to Purchase) set forth below, all pursuant to the guaranteed
delivery procedures set forth in Section 2 of the Offer to Purchase.
 
Number of Shares:
 
Certificate Nos. (if available):
 
------------------------------------------------------
 
------------------------------------------------------
 
(Check one box if Shares will be tendered by book-entry transfer)
 
[ ] The Depository Trust Company
 
[ ] Philadelphia Depository Trust Company
 
Account Number:
------------------------------------------------------
 
Dated:
----------------------------------------, 1998
 
Name(s) of Record Holder(s):
------------------------------------------------------
 
------------------------------------------------------
    Please Print
 
Address(es):
------------------------------------------------------
 
------------------------------------------------------
                            Zip Code
 
Area Code and Tel. No.:
 
------------------------------------------------------
 
------------------------------------------------------
    Signature(s)
 
Dated:
--------------------------------------, 1998
<PAGE>   3
 
                                   GUARANTEE
 
                    (NOT TO BE USED FOR SIGNATURE GUARANTEE)
 
     The undersigned, a participant in the Security Transfer Agent's Medallion
Program, the New York Stock Exchange Medallion Signature Guarantee Program or
the Stock Exchange Medallion Program, hereby guarantees to deliver to the
Depositary either the certificates representing the Shares tendered hereby, in
proper form for transfer, or a Book-Entry Confirmation with respect to such
Shares, in any such case together with a properly completed and duly executed
Letter of Transmittal (or facsimile thereof), with any required signature
guarantees, or an Agent's Message, and any other required documents within three
trading days (as defined in the Offer to Purchase) after the date hereof.
 
     The Eligible Institution that completes this form must communicate the
guarantee to the Depositary and must deliver the Letter of Transmittal and
certificates for Shares to the Depositary within the time period shown herein.
Failure to do so could result in a financial loss to such Eligible Institution.
All capitalized terms used herein have the meanings set forth in the Offer to
Purchase.
 
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<S>                                                         <C>
Name of Firm: -------------------------------------         -----------------------------------------------------
                                                            Authorized Signature
 
Address: --------------------------------------------       Name: ----------------------------------------------
                                                                                Please Print
 
-----------------------------------------------------
  Zip Code
 
Area Code and Tel. No.: --------------------------          Title:
                                                            -----------------------------------------------
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     NOTE: DO NOT SEND CERTIFICATES FOR SHARES WITH THIS NOTICE. CERTIFICATES
FOR SHARES SHOULD BE SENT WITH YOUR LETTER OF TRANSMITTAL.
 
                                          Dated: __________, 1998
