Good find, Jim. Thanks.
There's info about four more rinks at the end of the article you posted: "Besides Shimla there are only four other ice-skating rinks in the country, of which two are in Leh and one each in Kargil and Gulmarg. However, they are all outdoor rinks as the country so far does not have any regularly functioning indoor rink, said Banga."
I don't know anything about Leh and Gulmarg, but I believe Kargil is on the border with Pakistan because there's a movie called "L.O.C. Kargil" -- or Line of Control Kargil. They're probably all in the foothills of the Himalayas.