That's a interesting point about the critter fur. A couple thoughts:(Just throwing these out for comment)You will still have the same issue of sudden, frequent extreme temperatue changes. Camels and reindeer also grow winter coats and shed them for warmer temperatures. I don't think that we currently have any animals that undergo such drastic temp changes in such short amount of times. I maybe wrong about that but I can't think of any.
We'd have to look at critters who do endure big temp. swings. A couple that come to mind are (weird or silly as it may seem) camels and to a lesser extent, reindeer. I'm pretty sure camels could deal with things, I don't know how hot of temps reindeer can put up with.
I'm fighting for someway to make my open-range trail work, lol!
The other thing that occured to me is about the grazing pastures. Would the temperature changes effect those as well?? You would pretty much have to be providing most of the food for your livestock if we actually can figure out what they might be. I will think about it some more.