I tried CGI::Cookie with no effect on the results, still the page is displayed and no cookie is stored. The code now looks as follows:

#!/usr/bin/perl

use CGI;
use CGI::Carp (fatalsToBrowser);
use CGI::Cookie

$co = new CGI;

$cook2 = new CGI::Cookie(-name=>'test2', -expires=>'+1h', -value=>'sav
+eme2');

$cook = $co->cookie(
    -name=>'test',
    -path=>'/',
    -expires=>'+1h',
    -value=>'saveme'
);

print $co->header(-cookie=>[$cook,$cook2]);
print 'output';
[download]

Nothing changes either if I try to only use one cookie, nomatter which one of the two it is. ...-path=>'/'... has no effect on either - it defaults to '/' as I said before.