One of the problems with a tarp in the Winter is, when the snow melts from sunlight or warming weather, water will get between the tarp and the roof. Unless you use a very waterproof, heavy tarp (trucker style), that is what will happen. When the weather turns cold, the tarp will freeze to the roof. This will make a hasty exit to Texas complicated.:B
I'd suggest to do what your neighbors in the storage lot do and angle the trailer for quick melt-water runoff. That's what I do for the Winter months in MN and it works well (no tarp). I have one original vent cover on my trailer that is 44 yrs. old. It has never been covered but I did paint it a few years ago to extend it's life.
Depending on how much snow accumulates, you may want to think to the future about snow removal from the roof. A foot or two of wet snow adds a lot of weight onto the roof. I remove some of this with a roof rake made for snow removal. I can do that while standing on a ladder, I don't climb on the roof in Winter.