Quite true. However, the armies that made it as far as Central Europe were much smaller in size, breaking up into groups as small as the 20,000 I mentioned, or even smaller, but recombining as needed to fight major battles.
There is a persistent myth that the Mongols had huge armies, which is why their name for their armies, horde, came to mean a huge number.
In actual fact the Mongols were almost always considerably outnumbered by their opponents, though it probably didn’t seem that way to the opponents! The Mongols won by speed and maneuver instead of brute force, concentrating their forces quickly to achieve superiority at a critical point rather than across the board. The Mongols practiced a horse-powered version of blitzkrieg many centuries before WWII.
Yep, mobility and ruthlessness are an effective combination. War ponies with stirruped saddles, great mounted archers, and fairly effective lightweight body armor made them almost unstoppable by the enemies in their path.
There is a fictional recreation of Genghis wars. Its based on what they know about the battles but of course makes assumptions on the first person of the people themselves. They have a strong basis on historical fact and I thought very well written.
In the one battle where he used prisoners as a shield there were tens of thousands killed. The bodies formed a continuous trail for over 34 miles.