That's more of a stereotype than a fact.

It gets very cold in winter in the vast majority of nation, including the south and west. It snows in Las Vegas every year. Las Vegas even has a ski resort.† But people rely on an old cartoon-inspired vision of what a "desert" is, rather than the fact that "desert" means a place with little water, not necessarily high temperatures year-round.

Their vision of "American desert" is usually Monument Valley.†† But guess what, that's under snow right now, too. And it's not unusual.

† https://www.leecanyonlv.com †† https://en.wikipedia.org/wiki/Monument_Valley

Vegas and Colorado are neither coastal nor southern. My vision of "American desert" is probably near Albuquerque where I lived for several years. It snowed every year. But you'll note that New Mexico isn't part of the south either, despite its location on the border.

It's on the border between Arizona and Utah.