Falling from a horse in any circumstances is bound to be painful and dangerous. Add armour and weapons and you are almost screwed.

Though I doubt they ever reached what we mean by real gallop. All that weight is also felt by the horse and it would tire too quickly, especially if it had its own armour.


Fun fact: In my city a couple of years ago during the session of the city council a councilman put forth a proposition to commemorate a great historical battle by performing a full horse charge. It was to be done by reenacment enthusiasts. When it was proposed a man who belonged to one such group and a "horseman" by proffesion (he was asked to attend as an expert) stood up and disabused the council member, by saying that such a charge, in full gallop, with 100 untrained men and horses, equals, at least, 3-4 deaths and many more injuries. Which ended that proposal quite efficiently.

 

Knights used to cheat in jousts by either lancing at the horse rather than the opponent's shield, or in the older jousts where there was no separation barrier they concealed a spike under the horse's chest livery.

A problem with taking out a horse when on foot is that the horse is usually pretty heavily armoured too - considering the hefty investment they were - meant if you buggered up the initial attempt to break its knees or something they ran you over, kicked your belly through your neighbour's spine, bodychecked you into your mate's spear or other assorted equine murderous fun.

 

There's also some concern of the horse/rider still colliding with you? It would depend how you kill/injure the horse and if you're mounted yourself, but it's not a safe solution on its own. Unless we're talking about killing the horse from afar with missile weapons.