I took my cat with me from Boston to California when I was there on a one-year work assignment. He flew on the plane (not in the cabin me with) and was stressed but was ultimately fine. The way out there I gave him some kitty tranquilizer the vet prescribed but I skipped it on the way back and I think he adjusted better without the meds.
If you're opposed to the flight then a 3-4 day drive sounds like a good alternative. If you're worried out weather maybe consider renting a 4-wheel drive vehicle. If the flight's not direct they may not allow your dog anyway during the winter.
There's also an airline dedicated just for pets
http://petairways.com/