Horses are recurring animals in The Legend of Zelda series.
Ocarina of Time
Horses can only be found in Lon Lon Ranch, either in the stable or out on the main field. As Child Link, they can be seen running around on the track. It is only possible to ride horses as an adult however. There are only two horses that can be ridden in Ocarina of Time, Epona, and one of the ranch horses during Ingo's Horse Race mini-game. Ganondorf also owns a horse, as can be seen in the opening sequence of the game and after Link has collected the three Spiritual Stones.
There are multiple horses seen in Majora's Mask, including Epona, Cremia's horse, and the horses belonging to the Gorman Brothers. Epona can be seen in the opening sequence of the game, before being stolen by Skull Kid. She is later found at Romani Ranch.
Only a few horses are present in Twilight Princess, Epona being one, along with Telma's horse, which can be seen during the escort mission to Kakariko Village. Epona can be ridden right from the get-go in this game, first getting action by herding goats for Fado during the opening portion of the game, and later on for a Piece of Heart. Twilight Princess is one of the only games in the series where Ganondorf seems to own a horse, being present during the horseback battle at the end of the game.
The Minish Cap
Epona returns once more in The Minish Cap, but this time she cannot be ridden by Link. She can be seen in Hyrule Town with Malon, after the door to the ranch house has been unlocked, carrying milk that is purchasable by Link.
Breath of the Wild
"These can most often be found on plains. Their usefulness as transportation has made them valuable since ancient times. That said, wild horses do tend to get spooked and run off when approached, so if you're looking to snag one, it's best to sneak up on it."
In Breath of the Wild, horses (001 in the Hyrule Compendium) can be found throughout Hyrule, particularly in fields such as Hyrule Field or the Faron Grasslands. In order to ride horses, Link must sneak up on one and then mount and tame it at the cost of stamina; the higher the stats of the horse, the more stamina it will require to be tamed.
Mottled white/brown/black horses require little to no stamina to tame, albeit they have the lowest stats available in the game. Solid-colored horses tend to have better stats, and some can be considered among the best horses in the game. To date, no wild horse in the game has ever been found to have 5-star stats in all Strength, Speed and Stamina gauges (though the Lord of the Mountain is assumed to have perfect stats, it cannot be registered in a stable, so its stats are not visible).
To keep a horse, Link must register the horse at a Stable. Only five horses may be registered at time; to register a new horse once the limit has been reached, one must be let go. After a horse has been registered, it can be named and is equipped with a saddle and bridle. A registered horse's location is marked on the world map and it can be whistled for as long as it is within hearing distance.
After registering the horse, its stats can be viewed while boarded at the stable. For each horse, its strength, speed, stamina, and temperament is documented. Also recorded is the horse's bond with Link. The higher the bond, the more obedient the horse is to Link. A horse with a high bond will travel along roads without needing direction from Link. To bond with a horse, Link can feed the horse fruits (carrots and apples are favorites) and should also soothe the horse during a ride when it is particularly obedient.
In addition to the standard wild horses, a few special horses can be found in Hyrule: the Giant Horse, the White Horse, the Lord of the Mountain, and the Stalhorse. The giant and white horses can be registered while the other two cannot. Other tameable animals like stags and bears can be ridden to the stables, but cannot be registered either.
Epona cannot be found within Breath of the Wild, but may be obtained when the player scans certain amiibo. The Super Smash Bros. Link and the Twilight Princess Link amiibo will drop Epona on the first scan only. Other amiibo, such as the Super Smash Bros. Zelda amiibo, may drop Epona at random. She can only be received once per amiibo and must be registered at a stable in order for Link to keep her. However, Epona can be received multiple times from different amiibo, and each Epona received may be registered making it possible to have more than one Epona in Breath of the Wild. Epona has her own saddle and bridle that cannot be changed, and her bond with Link is already maxed out.
Horses can be killed by the player or during combat, but unlike other animals, they drop no loot. Registered horses that have been killed can be revived by the Horse God Malanya at Malanya Spring in south Faron once unlocked.
Horses can be customized at a variety of Stables, including the Outskirt Stable, but their bond with Link must be at max before this can be carried out. Every horse except the Giant Horse and Epona can change their saddles and bridles, which can be obtained in different locations around Hyrule; aside from those, the Royal Bridle and Saddle may only be worn by the White Horse.
Additionally, Link has the option to change the style of his horse's mane, if he so desires. There are ten styles, listed below: