FWIW, I bought a 2003 truck camper in 2004. Until last winter, I have always stored it outside here in Western NY. Lots of snow, cold, and rain as you can imagine. I always covered it with a silver tarp & lots of bungee cords. In the 12 years I stored it outdoors, I went through 2 tarps. They got a rip here and there every year, but some Gorilla duct tape usually fixed them up.
I never had any problems with moisture in the camper in all those years. In fact, one year I was late getting the tarp on it. It had already snowed, thawed & refrozen (late Nov), and the camper had a couple inches of ice on the roof. I put the tarp & bungees on it,trying to keep any more snow off it. It warmed up a bit a couple weeks later, and I took the tarp off to let it dry out. Man was I surprised when I saw the ice was gone and the camper was completely dry!
I don't believe for a second that a plastic tarp will cause moisture problems. Even bungeed on, there's still plenty of airflow to keep things dry.
I now have a heated pole barn I store the camper in, so no need to cover (or winterize) anymore.