mongols aren't that tough if your army is cavalry dominant. What you have to do is quickly, charge all of your cavalry at the horse archers who will be seperated from the main battle group alowing you to wipe them off without enemy infantry getting into the mix. Their melee cavalry will probably try to intercept you, but if you have enough cavalry, you can plow through their cavalry easily since they will be seperated. Once the cavalry is gone, the mongols are a piece of cake, just engage them in the front with your infantry and then charge in their backs with cavalry.

If you don't have cavalry dominant armies, then just sit in your castles and hope you don't have to sally once the mongols besigege you