Mongols didnt really have knights but even so rode with far more horses than knights. Even the poorest would have expected to have 5-10 when out on campaign and officers could have dozens. Also the horses the Mongols rode would not have carried a knight in armour because they were generally much smaller and didnt need fodder in the same way west asian horses did.

Yes, My main point (which I didn't say explicitly) was that the Mongols were much more self-sustaining as their horses could graze on the steppes without significant logistical support.

The Mongols did have 'knights'. They adopted Cataphract style just as other step people did. Their armor was as good or better then European knights armor of the same timeframe. Mongol horses were actually pretty damn strong even when not quite as big as Western war horses.

They were using 3-4 horses per rider.

And I think that they weren't farmers but instead nomadic herders?

This pattern far predates Genghis Khan. In the historical record alone, there are multiple waves of steppe nomads conquering agricultural civilizations including the Huns and multiple Turkic cultures. Prior to written history, the ancient cultures of the Pontic Steppe spent centuries breeding the modern horse; these are the same people who probably spoke the Proto-Indo-European language and included the male line ancestors of virtually all European populations.

The invention, and still more the dissemination, of the stirrup is closer in time to Genghis Khan than to the early Indo-European cultures, though.

Sure; mounted warfare existed for centuries before stirrups were invented. Actually it's not entirely clear whether the Proto-Indo-Europeans actually rode the horses or just used them to pull chariots.

Did mounted warfare exist before stirrups? The bronze age was all about chariots, and had little or no mounted combat. I'm not sure if that was because of a lack of stirrups or because horses simply hadn't been bred large enough.

The big question is of course whether Alexander the Great's famous hetairoi used stirrups or not. According to [0] they're considered among the first shock cavalry, and yet I can't find anything about them using stirrups, so clearly mounted combat, including shock cavalry, must have been possible without them.

[0] https://en.wikipedia.org/wiki/Companion_cavalry

Eastern Europe adapted to this and also used mostly cavalry tactics, some countries all the way up to early 20th century.

What works better (cavalry or infantry) mostly depends on population density, distances between population centers and road network. Less dense, less wealthy countries with large open spaces prefer cavalry. Urban, densely populated countries with good infrastructure prefer infantry.