No way you're leaving Jan 1 and will be golfing Jan 2 or much on the 3rd in AZ.. more than 15 hours a day is suicide, even with two drivers on that route..
Your direct hypotenuse path would be fine in April, but as Bill McBride said, definitely iffy in Jan..
OK & North TX I'd forecast will be an ice storm or at best just freezin with a 2-3 club wind out of CO.. The NM & AZ Mountain passes will need to be checked, and you won't make good time unless you're blessed with clear weather and nothing bad has happened soon before.. bring your winter survival gear..
Plan B, the southern route "south of dallas" through Austin or even Houston will at worst be rainy.. or clear dry cold.. depends how much moisture the southern jet stream is bringing in from the pacific across mexico..
Good luck.. If you're ever in Spring, TX.. ..
Look us up..