Horses - horses are fragile. William the Conqueror lost 12 at Hastings, as I recall. D&D horses are extremely tough compared to 1st level characters. They, and many other animal stats, seem scaled for a world where normal humans are ca 3rd level. Bucephalus is an exception, not the rule.
Attacking a mounted combatant's horse is a valid tactic that can often work, but I would disagree with calling a warhorse "fragile." 900 years of elite mounted cavalry (extending well into the age of firearms) would likewise disagree, I think.
William had something like 2500 mounted knights at Hastings. If he only lost 12 horses, he would have had a much higher survival rate among horses than he did among his knights. (Frankly, I'd bet he lost a whole lot more than 12, but that's the nature of the combat--not because the horses are especially fragile.)
[Funny you should mention Hastings--I was there on Saturday, and saw the battle reenacted. Frankly, all the action involving horses was pretty disappointing--precisely because they aren't fragile. If a reenactor knight does anything other than ride up vaguely close to a reenactor footsoldier, they run the real risk of the footsoldiers being seriously injured or worse by the horses (just by accident--and even with the footsoldiers in full armour with shields and helmets). And if the footsoldiers do anything more than vaguely wave their weapons toward the knights, they risk spooking the horses and getting the same result. So the cavalry charges--the real action of the battle--weren't especially exciting.]
D&D horses are tough compared to 1st-level characters, but that's as should be. Ever stand next to a shire horse or clydesdale? Massive and powerful. Easily capable of killing a man in a single wave of the hoof, and of taking far more punishment than most people. I would not want to face one that was trained for aggression.
That said, horses suffer in D&D because, unlike characters, they don't readily scale. Unless you're giving it class levels and loading it up with magic items, a horse is a pretty poor mount for a high-level character. So you start with something that is overpowered, pass through a relatively narrow band of play in which it's reasonably powered, then see it become proportionally weaker and weaker.