Might be associated with worse air quality however. Denver is particularly bad in terms of ozone.
“at high altitudes, atmospheric pressure is reduced, and oxygen is less available (commonly referred to as the air being “thinner”). This has a couple of effects on air quality for the people in the area. First, combustion engines perform less efficiently than they do at lower altitudes, causing an increase in emissions. Second, UV rays from the sun have a greater impact at high elevations, leading to an increase in photochemical smog, the result of airborne pollutants reacting with sunlight.”
https://www.aprilaire.com/blog/altitude-and-healthy-air-air-...
We also have to consider that temperatures feel different at altitude (and the mountain west is generally very dry). A dry 20F at 10k' feels more like 40F at sea level on the East coast.
Regardless, high altitude cities like Denver, Salt Lake City, Reno or Boise are neither particularly cold or cloudy when compared to other US cities.