Today in my history class we were talking about current Mongolia and it's agricultural and writing system, which was in Russian characters. From what I remember about ancient Mongolia it was basically all Chinese in and out so why would they switch to Russian?
The simple answer is that Mongolia never had a Chinese empire. The Yuan during Kublai and after had a Chinese bureaucracy and absorbed a lot of Chinese culture, but at its core it was Mongolian and Yuan rulers and nobles took great pains to maintain their own ethnic identity and to separate themselves from the Chinese. The Mongol script at the time was based off the Songdian/Uighur script - in all official documents of the Yuan Chinese and Mongolian script was used at the same time. The reason why Mongolia switched to Cyrillic was due to the Soviet Union - Mongolia at the time was a satellite state of the USSR.