Saddles are items from The Legend of Zelda: Breath of the Wild. Link can equip them onto wild horses that he tames. He can buy a default saddle from Stables when he registers his horses along with the default bridle.
Saddles like the Extravagant Saddle can be obtained as rewards after successfully completed mini-games. Others like the Traveler's Saddle can only be obtained by using the amiibo Rune with the Link Rider amiibo of Breath of the Wild series. The Monster Saddle can be purchased at the Fang and Bone for 299 Mon. The Royal Saddle can be obtained as a reward after completing the quest "The Royal White Stallion". It is automatically equipped to the White Stallion by Toffa, but Link can equip it to other horses since the White Stallion is equipped with the default saddle once registered.
Some special horses, like the Giant Horse involved during the quest "Hunt for the Giant Horse" and Epona, receive unique saddles on being registered and like the default saddles does not show up in the Key Item menu. However, these saddles cannot be changed. The Stable hands state that the Giant Horse large size prevents other saddles from fitting it. Moreover they state that Epona will not like Link to change her mane, bridle, or saddle despite her gentle temperament.
List of Saddles