If the early winter is any indication, you'll be in luck. Realistically, winter weather in the High Country is always highly unpredictable. As long as temps are low to mid 30's or colder, the ski areas and tubing runs will still be making snow. So even if you don't see the "real thing" falling, chances that you'll have snow on the ground for sliding are usually pretty good.
But then it could rain for days on end. You just never know in NC.
Ray's Weather Center is a good place to get current, past and future weather info.