Towing 5th Wheel from IL to PHX in March

So are you going to PHX as your title says or Tucson? Makes a difference.

the area to watch the weather forecast is from Illinois to Albuquerque. After that, pretty much clear and sunny. but even I 10 can get a snow/sleet storm between El Paso and Benson, AZ, so just pay attention to the weather news.
If you see it coming on the weather radar of your phone, stop at a rest stop or in a town, etc and let it pass over you. We ran into a heck of a sleet storm in west texas several years ago out by Van Horn. We just spent an extra day in an interstate rest stop.

x2 drop down to I 10. much better weather.

All depends on the weather forecast at the time. That same route may be fine. But if winter storms are forecast for OK, TX panhandle, or northern NM then you should probably head farther south to get to I-20 or even all the way down to I-10. Being weather aware should dictate your decision.