I would be saddened to see the courser loose HP. Largely because, as things stand, it goes down in about four or five arrow hits. In "the real world" (whatever that is), that might be OK, but in cRPG it isn't--not with the number of archers and their high rate of accurate fire.
Then again, if the cheap horses just got an HP buff, but retained their speed/maneuver, they'd be a bit OP. Still like ninjas, but now with MORE HP!
I counter-propose the entire idea of cavalry in cRPG be reworked! HP/Armor buffs for everybody, but speed nerfs everywhere. Less ninja shit, but more trampling of bitches and stand-up, horse vs man fights. I tire of hiding behind the reach of my heavy lance, and the speed and stealth of my courser.