Ruidoso is pretty far south; we stop over there at least once a year. Until you get up into the mountains, snow is not generally an issue. There are several major highways into the area, so they are probably kept clear...unless you drive there DURING a major winter storm. If you stay at a campground along one of these highways, it should not be a problem.
I don't know what the road up to the Apache Ski area is like, so you may need chains. I would be more concerned about THAT part of the experience with 2WD than towing into an area RV park. Maybe their website (or the Ruidoso Chamber of Commerce website) has answers, or at least a phone number for you to talk to someone.
If you have heated tanks, then you'll probably need to turn on the tank heater at night. Just remember to disconnect and drain your water hose at night and just go off your onboard fresh water tank.