Florida can be a no win situation what with the strong sun and the salt air. I can see where leaving a car covered for long periods could cause a build up of condensed salt (water) and cause problems. OTOH, my dad always parked outside and the sun and salt finally took the paint off the roof of his car. If using the cover, I'd think you'd want to take it off and dry it out once in awhile, and also wash the car frequently and make sure it's dry before putting the cover on. I may be mistaken, but I think some car covers can be washed too.
I guess if I lived there and didn't have a garage or carport, I'd just try and find a place to park in the shade, and not worry about the rain part of it.