I'm in your camp. Anyone who thinks there is a lot of game in the high mountains during the winter hasn't spent much time traveling them then.
All the elk move down as the snow makes finding food and moving about more difficult.
On our Washington passes, I've seen the snow accumulations of over 10 feet.
Even down much lower, around the winter of 69, when the snow was only around 5 or 6 feet in the Okanogan area, many were trapped by it.
Using snowmobiles (a relatively new thing, then), you could only go, say, 20, then had to dig out for another run, as you tried to get supplies to those stranded on their farms and such.
Now imagine those creatures with long, pointy legs and hooves trying to move about in that thawing snow. People wouldn't fare much better.