Hot Springs, AR to Tucson, AZ

They all work but some have nicer scenery. West of Dallas, I like Hwy 180 through Carlsbad to El Paso, with the wonderful view of Guadalupe Peak. The road is about as fast as the interstate with much less traffic. After El Paso, you will be on I-10.

Take any of the interstates to get to Tucson, they all work.

The only 2 logical choices are taking either 40 or 30 out of AR. 30 to 20 to 10 is the shortest and the one that gets you South as fast as possible.

Simplest way is I-30 to I-635 on east side of Dallas, at I-635 drop down to I-20, and then I-20 to I-10 to Tucson. Do Dallas area mid day or weekend and you shouldn’t have any problem.
Mid December rarely a weather problem across north Texas.

Also come back 1st of December so we will know what it really going to be like. We had a hot and a lot of wind this summer which usually means a cold hard winter.

i'd want to get south as fast as possible in December. I-30 to Texarkana and then, depending on weather and local road conditions, either I-49 all the way south to I–10 or stay on I-30 to Dallas then I-20 and on to I-10.