I second the Dolly Sods Wilderness. Very nice area, especially when isolated in the winter.
I was out there for a few nights in late February last year, and I was fine with very basic 3-season gear. A few inches of snow, and temps in the 20s, but nothing that merited 4-season gear, crampons/spikes, or anything of the sort.
Southern AT is always good; but I've typically found the VA sections to be fairly dry in the winter.
For a little closer to home, consider the Cumberland Gap too.