Laramie is actually #7 of the top 25 coldest cities in the US. Casper is #19, and Rock Springs #20. That should give you an idea of what you are in for. Link
The record low temp for WY is -66 degrees in Riverside. Only two states in the US have recorded a lower temperature; Alaska and Utah. The record low temp in Utah was at almost 1600 feet higher elevation and Alaska's lowest recorded temp was North of the arctic circle. The WY record actually ties the record low for Fairbanks, AK.
Both Laramie and Cheyenne are at least 10 degrees below freezing right now.
Still wanna go?
You might get by in a lesser RV than what people have mentioned but you'd need to take precautions to keep pipes and tanks from freezing up. At the very least, I wouldn't by an RV with a furnace under 42,000 btus or you'll be cold a lot.
There are other threads that go into detail so do some searching and you'll find what you need.
* This post was
edited 02/24/12 12:09am by jdiffend *