A handful of years ago, we had a hail storm that cracked one of the vents on our HTT. I did not have the time to fix it and we had no plans to use it the rest of the winter, so I put a tarp over the trailer and left it till spring. I bought a 20x30 that covered the HTT fine, but its flapping in the wind did wear a small spot on the edge of the roof.
I think one of the big differences between a tarp and a cover is that a tarp gets rigid in cold weather. Combine that with wind and it can cause problems. If you can keep the tarp tight over the camper, it might not be as big a potential hazard. Covers I have seen do not get rigid. Good covers are also breathable, so they do not trap moisture.
-Michael