Honeybear Campground in Boone, NC is open on a limited basis during the winter. They do have FHU sites. This is less than 30 minutes away and Boone is a nice college town (Appalachian State Univ.) with lots of things to do and see.
Grandfather RV in Blowing Rockshould be closer and seems to be open during the winter.
I have never been to these campgrounds, but Sugar Mountain is a nice place and also has ice skating and tubing run that is fun.
You might also want to check out Ober Gatlinburg for skiing. It is much smaller, but there are plenty of campgrounds in the Pigeon Forge and Gatlinburg area that are open all year.