For every one mounted soldier, there were 5 mares on hood, so yes enough milk was provided to the Mongol armies. On the other hand, most of the Chinese soldiers walked on foot, while the horses were used to lug all the supplies they needed. So the Mongols could move faster, more fleet-afoot, attack and escape more deftly. Their Calvary could slaughter the pedestrian enemy at will.

But fair enough, you’ve poked some valid holes in my somewhat entertaining thought exercise. Good luck to you.