In December, all of the E-W interstate highways north of I-10 are subject to snowstorms and high winds. I-40 might be an exception, but northern AZ, especially from the New Mexico border to Flagstaff can have the same conditions. If you don't want to drop all the way down to I-10 to go west, your only choice is to start watching the weather forecasts a week or more before your departure date and try to time leaving during a break in the storms.
Assuming good weather for 4 to 5 days, I-80 is the fastest and lowest elevation route (but be prepared to stop in Reno if Donner Pass is closed); I-70 to US 50 the next shortest but highest elevation route; and I-40 and I-10 to I-5 obviously the longest routes. There are plenty of motels and gas stations along all the routes, but Flying J is specifically set up for RVers, with RV-only pumps, dump stations, propane, RV parking, and a Denny's, Subway, etc., for meals. Little America truck stops along I-80 in Wyoming also have RV parking, cafes, and motels.
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