I80 is sometimes closed - such across the Sierras, or maybe middle of Wyoming. But I40 gets closed or dicy around Flagstaff. And I10 gets wind/blowing dust warnings. Plus getting to the 'southern' route requires crossing one of the passes in Southern California.
Any winter driving has chances of weathere delays. I've skated across Wisconsin when returning to Chicago from Mpls after Thanksgiving (that was in a 4x4).
My feeling is that if you can drive the car in Minnesota in December, you can drive it across I80. Even waiting out a storm will be faster than looping down to Arizona.