I've covered my TT with an ADCO cover for the last three years. The cover just went on to cover it for the upcoming fall/winter season. There has been no damage to the trailer as a result of covering it.
Where there are sharp edges where the cover rest on the trailer I put extra padding (cut up tarp) to diminish the amount of wear on the cover in those places. The cover is breathable, the straps are not pulled super tight (as recommended by the cover manufacturer) and I leave on window partial open to allow fresh air into the trailer during the off season.
When I remove the cover in the Spring I'm greeted by a clean trailer surface that isn't covered with six months worth of dust, dirt, leaves, bird droppings or other assorted stuff. In addition with the ventilation allowed by the breathable cover and partially open window there is no mold, mildew or bad odor.
The $225 I spent for the cover and the 30 ~ 45 minutes it takes to put the cover on or take it off in my opinion is well worth it. I much rather start the camping season pulling the cover off and finding a clean, ready to use trailer versus having to clean six months worth of crud off of it.