Oh! Well, there you go then! The further north you go, the better I-81 gets for you! I would definitely take I-81, and stay the heck out of DC/Baltimore/Philly/NYC! Even at 50 extra miles, you will easily save time/stress/money by cruising down the road!
I wouldn't worry too much about the weather. I've never encountered any weather on that route that I didn't also see on I-95. You will see your highest altitude around Wytheville, which is a little over 2000ft, then it's down hill from there. Obviously any winter weather would hit I-81 before hitting I-95, so it might be a timing thing. Just check the weather map before you leave home!
Happy trails!