Most of it depends on the tires you have...most RV'ers run a rib tread tire which is not a TRACTION tire, which is a requirement for winter travel in most places. Would you go driving for 8hours down a road covered with mud with your coach? I don't think it would be a very enjoyable drive. Snow/ice offers even less traction than mud.
If you want to run chains/socks on two wheels you would install them on the same axle, Once you lock the interaxle diff lock it doesn't matter which one. If you put the one chain on one axle and the other on the other axle you might as well have not put chains on, the differentials will allow the wheels with no chains to spin (unless you have cross-lockers)
I wouldn't say it is not possible to travel in the snow with your coach but my experience on the highway in the North-Western States and Western Canada (seen many southern trucks running rib treads come north and white knuckle it through a little slush while those that are prepared for it race along) has my common sense saying take the 4wheeler and enjoy the drive and when you get to the resort grab a stiff drink and relax in the hot tub or around the fireplace.
Also unless it is very warm (or Renegade insulates way better than Haulmark) it may not be overly comfortable in the coach and you will probably burn a pile of propane. Really shouldn't run the propane furnace(or any propane appliance for that matter) while driving.
I understand the yearning to go camping (I get the urge to go everytime I look out the back door and see my coach with 3ft of snow on the hood). I have also camped(lived) in a fifth wheel that was not fully equipped to winter camp and it was very inconvenient and expensive...
2007 Haulmark 3329DS, Freightliner Coronado Chassis, 515hp Detroit, Meritor Freedomline 12speed Autoshift, 10kw Generator, In-motion Satellite.