I've lost a couple battles vs. Mongols. For example, the last one was in the Crusades campaign when I faced two Mongol stacks with one of my own - just a regular stack, nothing specifically designed to counter them.

I haven't played all factions in the game, so maybe I missed some of the hardest ones, but I never felt like I was going to lose any of the campaigns. But then again, I don't recall losing a campaign in any of the TW games. I expect to win anyway, just as long as it's tense and challenging.