I do many trips in the NC mountains in the winter. I suggest Mt. Mitchell if your looking for some intense snow hiking. I hiked it 2 years ago during "snowmageddon" 2009 and it was amazing. Above 6000' we had snow drifts of 4 feet which is deep for NC. I hiked every inch of trail one weekend last January at Grandfather mtn. which is really nice too. Most of the trail up around Calloway and McCray's peak was solid ice.

The Linville Gorge is my #1 place to hike. I was up there last weekend and it was really hot around 90 degrees. Makes you wish for snow haha. That place can be borderline dangerous in deep winter conditions.

If your looking for some punishing winter backpacking I suggest the BMCT (Black Mountain crest trail). Its been called the "toughest" trail on the East coast. I hiked the 22 mile round trip route two weeks ago. It has several 6000'+ mountains and the trail is pretty rugged. In winter it'd be a 3-4 day hike due to the rugged nature and altitude of the trail.