I am also in Wyoming. We had over a week where we didn't see over -20 degrees, and then it soared into the negative teens for another week. A few balmier days came along, then it repeated the cycle. <sigh> I don't insulate my coop...even got into a discussion with about it with
@JackE and fortunately his wisdom prevailed.

This was our 4th winter since we built, and I don't regret not insulating or heating one little bit. Moisture control and ventilation are the keys. A person would think that sealing that coop up, warming it, insulating it, and all that stuff is the way to keep chickens safe. If you aren't planning on heating it anyway, what are you holding in? They keep all of their warm body air trapped next to their bodies. Oh, if you have enough chickens they'll also warm the air somewhat, but in my opinion not enough to justify the expense of insulation and a second, inner wall to keep them from pecking and eating it. I wasn't smart enough to build a Woods Style coop, which I regret, and our layout with a super high roofline pretty much means that there isn't enough heat generated by the chickens to warm the space. Dumb!
The only concession we make to winter here is to partially cover our run with clear, reinforced greenhouse type plastic. I say "partially" because we have a hoop run, and the plastic on the south side is a totally separate piece which we can roll up or down from the top just like a window shade, and then roll down and remove completely as it warms up outside. Most of the winter it's over halfway down, but on those super windy days when the weather is blowing in from the south or southwest, we roll it most of the way up. The north side also has a gap at the top of the arch, between the top edge of the run and the top of the people door. On the east side, we don't pull the large sheet of plastic all the way to the ground, instead leaving a small gap at the bottom edge. The first year we did the plastic, we sealed that puppy totally up. What a mistake! The floor was wet, the food was wet, and the chickens were wet. The top arch of the run was so loaded with condensation that it literally dripped down our necks when we went in there. Took forever to dry that out! We understood better then than ever before how critical ventilation is, even in the run. Moisture + cold = frostbite. That was the only winter a couple of my birds had frostbitten combs. Lesson learned, big time!
As for deep litter, I also use deep litter. There's a distinct different between deep litter and deep bedding. There are really good threads on here that address that very subject. Unfortunately either I have haven't figured out for sure how to find them or link them in this new format so maybe someone smarter than I can step in here. But remember that here in Wyoming, with our extremely dry and cold winter, composting in the coop slows way down. But either way, you'll find the chickens will sometimes make little hollows in the litter and pull their wings in, content and snug as can be. In summer mine do the same thing - but they'll lay their wings out flat over the edges of the holes to cool down.
In the end it's all about your personal comfort zone and what you think is best for your flock, regardless of what I or anyone else say. I just wanted to let you know that I'm in the same general area of the country, and we haven't found insulating necessary. Good luck! (By the way, we are in the Northwestern part of the state, 6 miles from the Montana border and about an hour and half from Yellowstone.
Edited to add: Funny, Jack...while I was typing you were posting! I do miss that little "new post notification" at the bottom!