Over the years, I've had the fortune (or misfortune) of traveling northern states during the winter. Naturally, it behooves us to watch the weather. Twice, I've been caught in lake effect snow storms in PA and NY which delayed my arrival between 2 and 4 days. Both times, I dry-camped in my 4 season camper at a rest area or private property with permission and stayed comfortable. Aside from being behind schedule, my propane bill approached the national debt. However, with few exceptions, I've found the Interstates to be reasonably cleared for travel.
When traveling in northern climes during the winter, I allow the sun to kiss the road for a couple of hours before getting under way. I also make it a point to get off the road before dark. Sorry I can't help with storage in VA.