Barton:
This year we went to Florida for January (left just after Xmas) and managed with no problems. We usually have a first night stop just south of Detroit, then Kentucky, Georgia, and an initial night in Florida. On the way back, we reverse the stops.
Lately, we've been able to winterize and de-winterize in south Kentucky, but it takes monitoring of the weather reports. One year, we didn't try it until Georgia. This year, the CG in Kentucky said that they hadn't been open the previous weekend because they were snowed up.
We always allow at least one extra day, sometimes two, in case the weather turns. The worst we ran into was in Ontario, when they were closing the 401 behind us and we found our windshield washer was full of summer fluid.