No lions have ever existed in historical times in Tibet. There are lions further south, in India, though, and, like with the common depicitions of "lions" in Chinese art, it appears that the iconography appeared in Tibet through cultural transmission. Lions have been powerful cultural symbols in other cultures that existed within the range of actual lions.

Asiatic lions were once common throughout India. Most of the range maps I have seen don't extend to Tibet, but certainly the extinct subspecies of lions lived in cold region including Siberia and they were also found in the Americas, meaning they crossed the Bering land bridge. So lions can live in snowy regions, though the northern subspecies should have all been long extinct by the time we are concerned with.

This question may be more suited to /r/askscience! :) I would cross post this there certainly