The place to learn Mongolian war arts is to study Ghenkis Khan. He was the first general of any army to develop special forces that specialized in tactical advantages by learning particular skills. He pretty much developed the "squads", platoons, etc. regimentation that armies follow, and I suspect that the information on his fighting methods would be found in that study.
If I can find the links again, I researched some really neat articles about his military methods and fighting methods a couple of years ago. He developed a code of conduct and was a tactical genius. Since recordkeeping wasn't a big deal at the time, there aren't many journals of their tactics or fighting methods. There is only history of what conquests he made, which was most of the Asian continent.