I tend not to overdo the provinces which will be attacked by Mongols - even if it's my territory.
Other than believing that no ruler would have known that they were coming at that date, I thoroughly enjoy the challenge of actually having them on board and dealing with them as a self-sufficient faction. With enough troops, you can just block the Horde as it arrives - kill as many as you like and put others to the sword. But where's a challenge in that?