You'll excuse me if I get on my high horse, once again, over the lack of satisfactory cavalry rules in Dungeons and Dragons.
Gary Gygax's original Chainmail rules recognized the advantages of fighting from horseback. In those original 1971 Chainmail rules, mounted warriors were three or more times as effective in combat than their foot-bound brethren.
But in DnD's transition away from Chainmail's mass combat rules, and towards the alternate d20 combat system, the importance of mounted combat diminished.
This is true of every version of DnD I own, and while I don't own a copy of the 4E rules, i'm willing to bet that mounts provide little or no combat advantage in the most recent version.
Mounted combat is a problem for DnD, of course. Certainly in the early years, much of Dungeons and Dragons was focused on underworld adventures, an uncomfortable milieu for one's horse. And there were significant dangers in leaving your favorite warhorse tethered outside the dungeon entrance, not the least of which was returning to find nothing but bones.
Apart from capricious DMs and their propensity for mount-related mischief, treatment of horses, as separate from a rider, with its own hit points, meant that horses became less useful as the character levelled up. While the character increased in hit points, his favorite mount did not. Therefore, as a hit-point sink, the horse diminished in value over time.
Games like Lord Of The Rings: Strategy Battle Game restore the combat advantages of fighting from horseback. Other games, like Avalon Hill's Magic Realm, don't go quite so far, but do provide some not inconsiderable advantages to owning a mount.
Magic Realm includes three categories of mounts: ponies (pictured at the top of this post), workhorses (above) and warhorses (bottom).
The pony doubles a character's movement in Magic Realm. For every move action that a character performs, she gets a free move action, by virtue of riding the pony. Ponies allow Magic Realm characters to travel quickly across the map, permitting them to visit the natives and find monsters and treasures. However, ponies are vulnerable in combat, killed with medium damage.
Workhorses are less vulnerable, being killed by heavy damage. For example, workhorses are invulnerable during encounters with giant bats, who can inflict only medium damage. Thus, a common opening day in the Magic Realm sees all of the characters gang up on, and eliminate, the Rogues, who possess a stable-full of workhorses that can be raided once the Rogues are dispatched. In addition to providing protection against giant bats, workhorses provide an extra move phase every day.
Warhorses are kept by the Order of Knights, residing at the Chapel. Warhorses give no movement advantage, but are tremendous and armored, making them very difficult to eliminate. Warhorses make characters well-nigh unkillable.