You think having cav is a disadvantage?? cav was the tanks of the medieval era i would look at how you use your cav.
I mean seriously cav will smash through any unit type apart from pike guys and for that you gott horse archers to wear them down . The only disadvantage i see for mongols and there cav is cav requires alot of micro to be used right so in essence you are going to have to be active all the time
Try making the enemy army split off to chase some of your cav then decimate them in small groups trying not to bog down you cav in prolonged melee which they then become weak . Hit hard hit fast then move (and thats just what the real mongols did lol )