There is a LOT of skiing in the continent of Asia.
Apart from the obvious Japan and South Korea.... there is skiing in:
China (for example Badaling)
India (Kashmir... for example Gulmarg)
Iran (several big resorts)
Turkey (resorts in the central part, and heliskiing in the north east)
Lebanon (resorts, but the country is fucked right now)
Kazachstan (only heliskiing)
Kamchatka, Russia (only heliskiing)