Your question is like "how far North do Pheasants range"? Depends on Winter habitat, snow depth, number of days of heavy snow cover.
For instance, in Mn not many pheasants say, North of Little Falls. Even though there's ton of good cover, cattails etc. The reason, 3-4 months of heavy snow depths.
Then when you go West to Western ND and Eastern Mt pheasants range to the border and into Canada a bit. Why so far North in that area? That area will get as cold as N MN. The reason is Snow depth, normally much less then N MN. But much more Winter Sun, melts off snow even that far North.
Same with elevation, Winter snow depths and length of time for heavy snow depths will be the limiting factor.
When I was at FT Carson in the early 70's there were some pheasants at 6-7 thousand ft. But it's a very dry climate.