Are you familiar with winter camping? Most RV's do not have usable water systems in the winter, as the pipes are not within the heated cabin and will freeze and burst. Even in RV units where the piping is within the heated space, it is still a LARGE risk to use RV plumbing in winter- Keep in mind that you will only have cab heat during your drive, which may not be enough to keep water lines from freezing in the back of the RV during mountain winters.
A forced air furnace will also take a toll on battery life if not plugged in- you can drain your coach battery easily overnight on a cold night just from running the furnace, leaving you with no heat at 5 AM... Walmart may let you park, but they may also have issue with you running a generator while parked.
Being truly self- contained in Winter is a difficult prospect.
We do the ski camping thing, in an old HI-LOW trailer. Its an older one with a hand-pump sink, which works well for winter as the fresh water jug stays under the sink (heated), and the sink drains straight to the outside- no tank.
We stay in RV parks that stay open through the winter, and use their shower and bathroom facilities. The costs are reasonable, usually $30-$40 per night. Our trailer has a stout furnace, and we also bring some plug in portable heaters to run off mains power.
I've also done the ski camping thing in a 25' C-class. The C-Class would burn a LOT of propane to stay heated- a 3 day weekend would burn through most of the propane in the tank (Note- it can be a real pain to find somebody to fill an RV propane tank out on the road- the process is different than a standard 40 lb bottle, and many people that sell propane won't be able to fill an RV.) Another reason to bring alone portable heaters- You pay for your propane, but if you are at an RV park, the electricity you use is included, and electric heaters will help fill in the drafty areas of your RV.
One nice thing about doing this in a motorhome- many ski areas don't allow overnight camping. The solution is to stay in the nearest RV park, get up at 7:00, unplug and fire up the RV, drive up to the front row of the ski area lot, park and go grab another hour's sleep while having secured rockstar parking.