At a recent TrailManor rally I posed the cover question to some very experienced and knowledgeable owners. The consensus seemed to be to not, repeat not, cover the trailer. The explanation was that the roughness of the cover would wear off the paint and cause more damage than protection.
Don't blame the messenger for the message.
I personally don't buy the argument for our situation. We store the trailer under a big maple tree and if you have ever seen what wet leaves do to any flat surface you would not want that to happen to the top of your trailer.
The compromise would seem to be to cover the trailer but don't let the cover touch the paint by some sort of a framework.
Dick