We went to the Grand Canyon last Christmas Holiday in our fifth wheel. We actually made a trip of it, stayed at Distant Drums RV park outside of Sedona over Christmas, great RV park. We checked out some wineries, Sedona, Jerome, the casino at Distant Drums, they gave us a nice Christmas gift, $$$. The weather there was great, some colder nights, but tolerable.
Then we went to Grand Canyon, Trailer Village RV Park, after Christmas for 3 nights. I think the low's were in the 20's and highs in the 40's. Burned through some propane, but no issues. Did loose the drain hose, I left it on after I cleaned the tanks when we got there and some water that was in it froze and broke the hose. We got snow one night, made the canyon look awesome. We liked camping right in the park because you are minutes away from the canyon.
It's the desert, so the weather can always change, and it's a dry cold, with the sun out 30 F in AZ is like 50 F in PA where I grew up on a winter day. Bring layers and sunscreen.[emoji16]
As others have mentioned the drive may be the hard part. Make sure you have plenty of days to get home if storms come through, we cut our trip early because a storm hit New Mexico and Colorado New Year's eve, snowed about 12" on I-25 and New Mexico does not plow the highways like Colorado does.
I would also check out Meteor Crater too if you have time. We stopped for about 2 hours and took the tour.
Good luck, if you go have a safe trip and keep the propane topped off!