Buying propane should not be a problem; the hardware stores etc. don't close.
Most campgrounds (at least in Vermont) close for the winter. Many of the few that don't are mainly or only open for long-term patrons. Most do not have full hookups because the campground water distribution system does not have heated pipes and would freeze; even if there were hookups, you'd need to have a heated hose or put it away every time after filling the water tank in the RV.
Roads are somewhat variable, but usually at least the main roads are cleared relatively quickly after a storm. One of the ways they clear them is through the use of copious amounts of salt. You would get road salt all over the underside of your RV, and this is rather corrosive. Typical RV construction is nowhere near as well protected against corrosion as typical car construction.
The weather in early winter is somewhat unpredictable. Often there isn't too much snow and cold until a little later in the winter, with a fair few days in December above freezing, but you never know for sure.
My advice, for what it's worth, would be to stay in motels/hotels, which have adequate heat and running water systems that don't freeze, and if you drive to drive something other than the RV. (Amtrak might be a reasonable alternative to flying or driving.) That said, it is not completely impossible to use an RV, if it and you are properly equipped and prepared for the weather. RVs do vary a good bit in their usability in subfreezing conditions.
