I'm sure it was frowned upon due to the expensive nature of horses... Are there recorded instances of this happening?
Horses were expensive, but most tournaments were fought between knights or at least squires and pages and other high-born people, so not the end of the world if the horse died financially-speaking. If a horse was killed in the sport naturally (accidentally), I don't think anyone would bat an eye or blame you. If, by chance, you intentionally tried to kill or injure your opponent's horse, that would be very frowned upon, and you'd be charged for the cost of the horse.
In the High Middle Ages, many times if you lost your joust, you would forfeit your horse, and potentially weapons and armor as a wager. Things were a lot more "down and dirty" in these matches, and I wouldn't put it past one of them to "accidentally" slip up and kill/injure your horse in a charge if it meant winning (but if you win their horse if you win, it's better to win without killing their horse)
Late Middle Ages brought about chivalry so there was an effort to win fairly, so taking a cheap shot at someone's horse wouldn't really be taken well. The idea was to "unhorse" the rider, not kill his horse.
Reference: Jousting in Medieval and Renaissance Iberia (little specific regionally, but gives you an idea) "If a knight makes a foul strike on the head or neck of his opponent's horse".... he'd have to pay back the full price at the discretion of the judges.