Moab is going to be pretty cold in January but doable and enjoyable as long as you are prepared for it. There are multiple nice RV parks although some are closed until mid-March.
I know Portal RV Park is open year round and I believe Spanish Trail and OK Corral are as well. Moab Valley RV Park is not open until March some time.
For visiting Zion NP, the temps will be much more pleasurable in January with an average of highs in the low 50's and lows around freezing. I would recommend Zion River Resort for the stay.
Mike.