I can't really comment on whether using the cover in the summer is a good idea or not. I've never done it, so I don't have experience.
The thing with cheap covers is you'll find they can tear easily in the wind. It's still wise to cover sharp corners of the trailer (like gutter corners, awning edges) with some foam pipe insulation (or just foam in general) to prevent the cover from ripping. It's a good idea to do regardless of the cover you have.
With all covers, it's important to have it strapped down tight. If it's loose, then you can get damage to the trailer.
My favorite style cover has like a tarp material on the top, front, and rear, where the sides have a breathable material.
I would see if you could put like some pool noodles or something up on the roof to give it air space to breath. Saw horses would work too, even though the cover may not be big enough, but it's a long way to get those up there.
