Horses aren't just well-suited to heroism. Horses lend themselves to tearjerking, too; if you want the audience to sympathize for the main character, well, just kill his poor horse, and that'll do it. Dances With Wolves starts to become gut-wrenching when Cisco, John Dunbar/DWW's horse, is killed out from under him.
Horses are, of course, a major factor in The Lord of the Rings. You have Gandalf, claiming for himself Shadowfax, the greatest of all horses, and one of the most heroic moments in the story – book and film – comes when the Riders of Rohan, a culture devoted to the horse, finally arrive on the scene at the Battle of the Pellenor Fields. Even the hobbits get into the horse act, with their use of ponies; Sam's beloved pony Bill, who gets turned away at the Mines of Moria, is long-missed, and Sam's relief many months later to discover that Bill has turned up back at Bree is a wonderful moment. And in truth, the fact that the Fellowship is mostly horseless seems to put them at a psychological disadvantage already, before they ever set out from Rivendell.
LOTR also gives us evil horses, in the black steeds that the Nazgul ride in the first half of The Fellowship of the Ring. In the film, Peter Jackson depicts this by use of close-ups of the horse, from strange angles, shots of the spittle dripping from the horse's mouth, and so on. And when the power of the river is unleashed against the Black Riders, the foaming waters take the form of white horses.
On the flip side of that particular coin we have the sacred horses of Stephen R. Donaldson's Chronicles of Thomas Covenant, the 'Ranyhyn". These horses are larger than their Earthly equivalent, and they are somehow in touch with "Earthpower" – the magic inherent to the world – and will not allow anyone to ride them that they themselves do not choose. One of the most potent moments depicting the power of Thomas Covenant comes when Covenant, as an act of atonement, commands the Ranyhyn to visit Lena, the girl he raped earlier.
Great horses are the key plot point of Guy Gavriel Kay's brilliant novel Under Heaven, when a distant princess decides to gift a relatively minor man with two hundred fifty of her great horses, an act which sends shockwaves across the dynastic rule of Kitai (GGK's medieval China). And let's not forget the Firemares of Krull!
Horses in SF? Well, there are horses aplenty in Firefly, which is fitting as the show is essentially a space western. There are no horses, per se, in Star Wars, but the Tauntauns of The Empire Strikes Back are rather horselike. In Star Trek V, there are beasts on Nimbus III (the "Planet of Galactic Peace") that aren't horses, but might as well be. (I think they're there because William Shatner, who directed that one, is a noted horse enthusiast.) Shatner's equestrian enthusiasm would be indulged again in Star Trek Generations.
Not SF or fantasy, but here's a scene from a good movie called Hidalgo, which has Viggo Mortensen playing a guy who, along with his horse Hidalgo, enters a race across the Sahara. I like this scene because it shows the beginning of the race...and what happens once the racers are out of sight of the people watching them start.
All hail the horse!