Many folks in New Brunswick travel south on the same agenda you have planned.
They stay here to enjoy Christmas with family and friends and then leave to head to warmer weather before January 1st (weather permitting) One friend likes to leave on boxing day with the goal of spending New Years Eve with his warm weather friends in Florida.
Most however travel at a more relaxed pace. The rule of thumb when heading south form here is plan to spend the first night in a motel. Hartford CT seems to be a popular first night stop By night two you should be far enough south to find some open campgrounds where you can dewinterize. That schedule is based on driving eight hours per day if you can handle it.
Coming from Northern NB adds travel time so you might have to spend two nights in motels before you get to an area with open campgrounds but the good thing is it is the off season and motels rates should be cheap.
Is your plan reasonable - yes and many are already doing exactly that. Just keep your eye on the weather and stop if conditions are slippery. As someone already said driving on bare pavement is the same winter or summer. Most times the roads are clear the day following a storm so delays, if encountered, would be minimal.
Good luck with your plans and safe travels