India did opt for snowmobiles. Dated news, and its not clear if these are still in use.Crampons:
With ice and snow setting in Ladakh, it is assumed the PLA would be equipped with add on crampons on the boots to avoid slips and falls.
Alternatively micro-spikes might work.
Russians seem to use crampons and on flat terrain they used to use skis, but now use motorized sledges instead.
These snowmobiles would still need fuel and special engine modifications to avoid altitude related power loss.
Also the terrain is not always flat like Canada. There are crevasses and rocks beneath the snow. The snowmobiles make a noise giving away the locations.