I'm an experienced RVer, and an experienced driver in snow and ice, having grown up in northern Ohio. The OP is from Virginia where I've lived for decades now, but I have no idea about how well he may handle driving in snow and ice.
There are two issues here, one being the driving in winter weather, the other being the RV water/heat/comfort situation. RVs are typically not insulated for winter camping. Not all RVs, mind you, just most. And I rather doubt the rental places pay the extra bucks for all-season rigs. A summer rig is going to be less than comfortable in temperatures below freezing simply because the floor, walls, and ceiling are going to stay cold no matter how much heat you throw at them via the furnace. This will make them feel cold even if you have the air temperature set to 80. That alone would make me go car and hotel.
That trip sounds like a great one, especially at that time of year. I'd love to see those places with snow. Just not in an RV.
