We live in Las Vegas and have made numerous trips to the Grand Canyon.
I have never gone in the winter due to the altitude around 7000 feet at South Rim.
We stay a Canyon Gateway RV Park in Williams, it is to the left at the first exit off I40.
Their phone number is 928-635-2718, I would call and check weather and temperature.
The Grand Canyon Railroad is near the park and is a memorable trip to the canyon on a steam engine.
Best wishes the Grand Canyon is AWESOME!
Golfnut