No. For security reasons cookies are limited to the originating domain.
AFAIK the only thing you could do is to run scripts on domain2.dk and domain3.dk that return 1x1 px transparent GIFs - and set cookies with the values they have been passed via URL.
You can then includes those images in the login/logout pages of domain1.dk so that the cookies will be set on all 3 domains.
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