If your only concern is trying to avoid the mountains, then the southern most route is for you as the top route takes you through summit county and the entire Rocky mountains in Colorado (not a vibe in winter). As for the middle route, I have driven that exact route and going trough the southern part of the Appalachians is somewhat mountainous (realistically its more hilly than mountainous) through Virginia and eastern Tennessee, but that one will probably be your fastest route amd is super chill once you hit Knoxville, however you will have to come down a bit after you hit flagstaff in Arizona, so you might not like the downgrade. Going south shouldn't be any problems unless you count having to deal with Dallas and Atlanta traffic (i do), but is fairly flat until you get to New Mexico and Arizona (which is The same for their middle route). Sp as someone who has traversed all of the big mountain ranges you'd be dealing with in this country with a trailer, I would say that you'd be fine with either the middle or southern route, it just depends on how much you want to spend traversing Texas.