I'm sorry RedTemplar but I think you're a bit naive about history.
The Mongols won so many battles for MANY reasons. Their superior archery destroyed the relatively poor steppe peoples, and their superior tactics (feigned retreats, ambushes, etc etc) benefited them as much as their cavalry. They used so many of them because they had so many of them; they were a steppe people!
You're also forgetting about the prevalence of *light* cavalry used by the Mongols. You're bringing light cavalry into a heavy cavalry discussion. The greatest advantage that horsemen bring to the battlefield is mobility. This allows for the above tactics, blitzkrieg warfare and in an emergency...additional food supply (horses).
You can see examples early on of intact shieldwalls holding back frontal cav charges. Just what I can remember from reading a Military History magazine shows that unbroken, disciplined infantry can stop horses cold. Even troops with smaller shields and few longarms.
Show me where it is said that cavalry was the main force in Europe. Cavalry was the most *important* force mainly because, as I said, it added mobility to the battlefield. Heavy horse was also expensive and therefore societies focused on ways to increase their availability. Infantry was the main force but cavalry was the most valuable.
Also remember that horses aren't stupid. They're quite crafty and don't want to die. Yes they were bread for war but no they didn't like charging into solid objects (trees, rocks, PEOPLE) making a lot of noise and waiving things at them.
You can see this in MTW, especially in VI. Once you are able to train large amounts of horsemen, the battlefield opens up to you.
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