One thing I should point out (in passing) is that the stirrup is not the be-all, end-all of cavalry. It is incredibly useful for horse-archery - allowing for a more stable firing platform while in motion, as well as (I think) a larger bow - but for a melee it's not so useful, nor for pure shock tactics such as a lance charge. For that, a good saddle was needed - the original 'blanket on a horse's back' just didn't cut it, really, but the four-cornered saddle provided much-needed stability in the seat, so you could swing a sword or thrust with a spear with relative impunity.

Stirrups also made it much much easier to get on horseback, mind! Vaulting onto a horse is not fun unarmored, and doing it in 40-60 pounds of gear is probably less fun yet.