Isn't Montana comparable in area to Germany, but has about 1% of the population? That itself makes it fairly fascinating.
Alaska is far bigger and has fewer people.
Yes but we all know why, it's an empty frozen land. Montana is located in a habitable region.
Marginally habitable at best. There's little question as to why Montana is so sparsely populated also. I was there in late June and it was still chilly. The highway through Glacier National Park was still closed for snow clearance, which was a major disappointment. The Eastern half of the state is just an extension of North Dakota, a dynamic that I'm sure you're very familiar with. The Western half is also extremely remote, but rugged also, which made for a fun vacation, but not a practical place to live. FWIW, Wyoming has an ever lower population density.
I was in the area twice. In late August 2010, the first time, and while it wasn't closed, I experienced temperatures around freezing on the main highway through Glacier (with light snow flurries). Fascinating place really. But probably not the most convenient place to live.