They plow the mountain passes in the winter time in at least Montana and Idaho. I'd be very surprised if they don't in Colorado or Utah.
If someone's not used to driving in snow, it'll be even worse. You should not let them drive if there's snow/ice expected in the next day; or the roads haven't been cleared yet. As someone who grew up in Minnesota, I can tell you that yes, we are better at driving in snow than people down south. However, we go in the ditch a lot anyway.