Welcome to the RTA Forum!

I'd agree that studded snow tires wouldn't be a good choice for this - or most long distance trips - even though it is quite possible you will see snow - even on your southern trip through New Mexico and Arizona.

As long as you have all-season tires, and are sticking to interstate highways, you should be fine. I'd much rather deal with being delayed for a day because of a bad storm, while you wait for road conditions to improve, than dealing with the hassle or driving with studs - or even worse, bringing extra tires to change while on the road.

I'll move this thread to the "share the gas" section to increase your odds of finding a co-traveler.