Yeah - armor doesn't help much when you're up against a people that grow up on horseback and are horse-archers of such skill that they can target and hit a helm slit. Add to that the fact that they were the first army to use what we'd recognize today as "modern" tactics and strategy and you can see why they went through almost all the Islamic and European armies that stood before them like a hot sword through butter.
Imagine if you will, a group of Islamic or European cavalry of the 13th or early 14th century. A band of small men on ponies gallops into range, looses some arrows at this force and then gallops away with the other force in hot pursuit.
Now, keep in mind that cavalry of the era tended to attack "on line", i.e., side by side abreast, in a somewhat disorganized charge. After the initial charge, it devolves into a swirling melee of men and horses - but pretty much it's all or nothing at once with such tactics. Roman cavalry tactics weren't that much better.
So, the Christians or Islamics crest a hill, and this is what they see on the other side:
The Islamics or Christians would suddenly discover that they were pretty much a bunch of amateurs up against the first true modern army in the world. Easy to see why my ancestors pretty much steamrollered most who stood against them.
The irony of it was that the Khan would have been perfectly happy to let the Islamics and the West alone, but NOOO, the Islamics had to be their usual chop-happy selves; they executed his friend, the ambassador that he'd sent in peace to establish trade.
I know where you coming from then. Play many computer simulations with Medieval Armies and the Mongols are the most difficult to take on, without a doubt. I thought that your ancestors were the Rus or the Novgorod. I have been simulating controlling my first Islamic Army. The Abbasid culture. Based in Baghdad at the time. The Kingdom of Jerusalem attacked me, and let me say that they asked for a ceasefire. Took out quite a few of their armies.
The most difficult scenario was the Knights Templar. Lost many Knights battling Cataphracts, but won the campaign eventually. Still have not figured out how to take on the Mongols. I have been mostly avoiding them in previous simulations. Fighting them at a river bridge crossing or besieging them within a city at least gives you a chance. In the open field, they are most difficult.