We just went in November and it was spectacular.
Cold at night but pleasant during the day after we were warmed by the sunshine.
Nothing was sold out, we found openings at all the campgrounds, even inside the park and at Dead Horse State Park.
We are already planning to head back down for the same time next year.
We didn't even see many cars at the most popular pull overs or scenic spots.
I suspect Jan or February would also be good although March might be somewhat warmer.
The only possible downside is that many of the services/restaurants/guides/tours in Moab were closed. Still, there were enough to meet our needs.
I have a trip report in the forum for additional details.
2008 SMB EB-52, Quadvan 4x4, 6.0 PSD SOLD
2017 Ford Transit T250 148WB mid-roof w/ Quadvan 4x4