Having spent four winters in Gunnison years ago, including one of the coldest and longest in recent history, I can say that there are much worse places in the winter. What makes Gunnison get so cold is its location in a "bowl." The cold air just slides down in there and stays. To do that, there can't be much wind--so, when its coldest (-30 to -50 F.), the wind generally isn't blowing.
Because Alamosa sits in a much larger valley, it's possible for them to have a little more wind while it's bitter cold.
Now, if you want true misery, go into eastern Montana, North Dakota, and Minnesota where--despite the ambient temperatures usually being a little warmer (say, 0 to -20 F.)--that can come with winds of up to 40 MPH. Also, while it's generally clear and sunny in Alamosa and Gunnison during the coldest days in winter, up in the Northern Plains it is often cloudy. And, of course, the farther north you go, the lower the sun angle in winter.
Finally, Gunnison got its title of being one of the coldest places in the United States as much because of its low minimum temperatures in the summer, as from its cold winter temperatures. It can freeze any night of the year in Gunnison. One year when I was up there, it got down to 21 degrees on the first day of summer, June 21st!
All that said, I would have loved to have seen Gunnison when it was a railroad town . . .