John,
I did a similar trip in November (South Bend, IN to Albuquerque, NM) and will be doing the same thing in a Budget truck next week. From what I gathered then, and even moreso now, you could run into decent weather or it could be miserable/unplayable depending on the day or week. I stopped the first time and played Rose Creek GC in Edmond, Oklahoma, more because it was a good stopping point than anything. Would have liked to have played Oak Tree instead, but that wasn't an option. Albuquerque has some nice courses and the weather is decent more often than not (despite yesterday's snow!). Tucson might be a little out of your way, but it would have better weather than going north through Flagstaff!
I didn't find much to play between Oklahoma City and Albuquerque. Hope that's at least a little bit helpful!