Camp Hale, Colorado, or a 10th Mountain Division (over which some Coloradans wax nostalgic), there were infantry "ski patrols" practicing on Mount Rainier, Washington.
This drawing is from a Life magazine article from its Jan. 20, 1941 issue. Those are GI canvas leggings, not "puttees," which were even more evil—something the Brits picked up in northern India and which we copied from them for World War I infantry battledress.
These are puttees.
I had wanted to be the last cross-country (Nordic) skier in Colorado with bamboo poles, but I broke the tip off one last winter.
Googling around, I find antique poles sold at high prices as decorator items. (More reasonable prices on eBay, however.) Various firms offer high-tech carbon-fiber poles wrapped with bamboo for an antique look.
But people are discussing how to find or replicate 1930s ski clothing! On the Internet, you are not alone.