Hahahah fantastic, I'm gonna try this out
Does it also go off as fast as it would on foot?
Yep. Exactly like this.
By the way, i tested those animations with lepintoi some days ago. Overheads/Thrusts only hit the enemy when u can manage to bump them while they jump straight infront of you (And that barely happens) or you stand still and sneak in from behind to make your horse kiss the enemies neck and then they can hit him xD
Right- and Leftswing don't hit the infantry unless they jump, too.
So, those animation are really useful to look awesome on your horsie and to kill other cavalry.