Naturally, you never know about weather and best to keep checking once you leaving Florida but I would highly recommend you take the southernmost route of I-10 to I-25 north into New Mexico to I-40 west.
I-40 can get very bad around Albuguerque and west in the winter months. 491 is wide open country so if it's snowing it would be a mess.
Unless you need to visit someone at this time of year, I wouldn't advise getting to Cortez. Good luck!
Full-timed for 16 Years
. . . Back in S&B Again
Traveled in a 2004 Newmar Dutch Star 40' Diesel