Yes, the Alpini where Italian alpine troops who where used extensively in both world wars. In the first world war they primarily fought against Austrian alpine troops and German alpine troops. What you are looking for is called "the war in snow and ice".

Forts where important features of the conflict with both sides engaging in a race to have higher forts and more complex forts dug into mountains. There are even accounts of troops using avalanches as weapons via artillery fire.

As a side note the actions that let Erwin rommel remain in the German army during the draw down of the interwar years by earning the pour le merite, happened fighting the Alpini in the Italian alps.