You can have that weather in northern Arizona though.
The closest thing we've had in a game to the temperate rainforests of the pacific northwest that a lot of the cowboys of the region had to fave would be the thick tropical jungles of Crysis and Far Cry.
And the leather soles get mushy...and the salt used to melt the ice absolutely shreds the leather just above the stitching when it dries out. Western boots suck in the snow, and it's a quick way to ruin them. Even rubber-soled ones like some of Ariat's don't last, but they're better on wet surfaces.
Those are riding boots, or dress boots. They also make Western style boots with rugged soles for work. I have a pair and they're outstanding on all terrain, including snow. Here's an example:
Cowboys are... prepared to exist outside - whatever could they have been thinking!? :-P
Seriously, each of those elements was intelligently designed for the purpose that cowboys had for them. I use many of those same elements myself, while people prepared only to sprint from car to indoors have a whole other thing going on.
And I'm sure I would have laughed at that cowboy had I seen him while I was wearing actual winter clothes. People's brain just freeze come winter time and they become too dumb to dress properly.
Not American but doesn't central America get cold as fuck at night? I would assume that's what cowboys dressed for since you can always remove clothes but you can't exactly create them from thin air at night.