Two things come to mind. Firstly, are you sure that Apache2::Cookie is being loaded (not just installed on your machine) when your apache server starts up? Perhaps have a look at your startup.pl file?

It *used* to be the case with mod_perl 2 that you could arrange for it to be installed in a separate "Apache2" directory (so that it's modules could co-exist with modules of the same name in mod_perl 1). Then, in order to use those modules, you'd have to say use Apache2 in your code first. This would fiddle with your @INC so that the remaining mod_perl2 modules could be used.

That all stopped when the mod_perl 2 modules were renamed (sometime around 1.99_22 IIRC). Perhaps your server has been set up in this way?