I use a good quality 1/2 car cover on a convertible kept outside during the winter months (not using the car much)
The interior does suffer from condensation, although there no obvios damp or leaks (carpets etc dry). Would leaving the windows cracked open a little help?
I wouldnt open them personally with the cover on, best way is to air the car really on a fine day by putting the roof down. Even slight leaks make a difference as the condensation builds up and makes it worse, getting the interior dry is critical.