I would say it depends or is negative. I don't live in the US but here in the german alps, most towns/cities are not on top of the mountain. They are wedged between the mountains. In my city that means the sun is setting at 1 pm in the winter because it gets blocked by mountains. I had no idea about this before moving here but I have to say it gets annoying. There is also a city close by that has the highest suicide rate in Germany. They get even less sun in the winter because the surrounding mountains are higher.
The US is generally at significantly lower latitude than Germany and other mountainous areas in Europe. This means that for large parts of the high altitude areas, seasonal variation in day length is much less than in Europe.
Also, because urban environments in the US west are relatively new, they tend not be found "between mountains" in the same way that the centuries old cities across the Alps etc. are. The large population centers (Denver, Salt Lake City, Albuquerque) are built in large, open flat areas, and many of the midsize cities are not really surrounded by mountains in the way that equivalent European or other non-American cities often are.
I would assume that higher altitudes would have more intense winters that then result in people staying indoors and isolated for longer periods of time?
I would guess that altitude and longitude are not correlated globally (at least I don't know why they would be) but in the US I generally associate altitude with snow.
Countries like Finland and Iceland are consistently in the top 5 of happiest countries in the world. Of course that has many non-related reasons, but the effect of intense winters can't be too bad.
Finland and Iceland also have some of the highest suicide rates in Europe. It seems that the correlation between happiness (or well-being) and suicide is complex.
Which makes sense: it can be isolating if everyone around you seems to be thriving and you aren't.