Well this is purely from memory, I will have to look for the book later.
Far from being a Horde of maniacal bloodthirsty gits (which they were) the Mongols also had an organised military system based around the Regiment (Tuman).
I cant remember the exact structure but it reflects modern day and Roman usage, eg sections, platoons companies etc. Each man was equipped in a similar uniform and each carried a composite bow and sword.
Mobility was the essence of the Mongol war machine, as was rapid penetration of enemy lines and communication over great distances to coordinate the force.
In essense it was a Blitzkrieg style of warfare. Mongol armies would separate, penetrate deep behind enemy lines and go for strategic points, often recombining their armies at just the right moment for battle. Each warrior/trooper had several mounts and would change them frequently during these mobile operations.
I find it fascinating to see the same apparrent discoveries made through the ages. Blitzkrieg is the same in essence whether you use a horse, a tank, or a hoverthingy…