Appalachian Ski Mountain is about 45 minutes from the cabin. You can go on main roads via Boone, then to Blowing Rock, or you can take the scenic route over the mountains. Both are about the same time.
There are five runs and an ice rink, and it is not expensive to rent equipment for half a day or so. Or pay just one dollar for the car park and watch all the antics from the comfort of the ski lodge, which has a restaurant, shop - but no bar.
The Hawks Nest is slightly nearer to the cabin and also has a golf course with a bar/lounge in the ski lodge. There is also a snow tubing run.