My experience here, going on 9 years now, is unless we get into a weather cycle, January is pretty mild, just brutally cold. Although I seem to always have some meeting or class or something to get to in January, and miss it because of ice on the road from a previous night’s snow. And February is the “no snow” month.
That's a good thing. As long as it's not so cold that I need a block heater, and as long as the roads are fairly clean, I don't think this trip will be terribly problematic, as long as it's carefully researched, budgeted, and planned out. And, honestly, the really big worry that I have is mechanical breakdown, which is why I will have my car inspected and serviced prior to the trip.