For some winter solitude, take in the G.R. Thompson Wildlife Management area during a winter snowfall.
The G.R. Thompson is a piece of public land in Linden, VA, thats primarily used by hunters. The Appalachian Trail runs right through this section and visiting during a fresh snowfall can make for a great adventure. Only 60 minutes drive from greater Washington DC area, this is an easy adventure! Distance is completely up to you, based on your tolerance for the cold, and how much you're wanting to hike.
Park at the Trillium Trailhead parking lot, which links up with the AT.