You mean Suutei tsai. It's actually more of a soup than just tea. And milk is just one available ingredient :
http://en.wikipedia.org/wiki/Suutei_tsai
An old tradition among many Mongols was to not drink water straight. This could have been a result of the Mongols’ belief that water was sacred. It could also have come from the need to conserve water
> There are some Sri Lankans who do that due to the British influence and I imagine in India as well, but that's not the case with most of the tea cultures.
I wonder where the Mongolians got their milk-tea from. Probably not from the British.