I have done the transition several times. From CA to OK, OK to AZ, AZ back to OK. The one thing I noticed was I had to start feeding concentrates because the hay out here is not even CLOSE to what I could buy in AZ. I pretty much consider the prairie grass hay out here to be forage and that's about it. I feed Strategy GX or Omolene 400 since we've been in a drought and even that hay is scarce.
The first winter or 2 I was out here, they didn't get enough coat, so I bought several different layers of blankets. I started with a sheet, then went to mid-weight, and finally mid & heavy weight during the ice storms when we were in the teens below zero. They did ok, but still lost more weight that I liked. The last time I came back to OK, we built a barn and that helped immensely. So, if you do have to come back, if you don't have a barn, I'd board her in a nice barn for at least the first winter and then in spring put her out on pasture.
We're getting down to teens & 20's here in OK, MO is colder.