"A mysterious saddle made with forgotten ancient technology. Equip a horse with this and whistle to call them even when they are far away."
The Ancient Saddle is a piece of Horse Armor which appears in Breath of the Wild and was released as a part of the second DLC expansion for the game: 'The Champions' Ballad'. The Saddle, along with the Ancient Bridle, are acquired as part of the EX Ancient Horse Rumors side quest. When equipped, it lets Link summon his steed wherever it is. However, some horses, such as the Giant Horse or Epona, are unable to wear the Ancient Bridle.
Over at the Highland Stable, Link will find the Super Rumor Mill V3 on the table, which hints at the location of the Ancient Saddle. The rumor mill hints that the Ancient Saddle is located at a spring where the horse spirit resides. The hints refers to the Malanya Spring, where the horse God, Malanya is located. The spring can be found just southeast of the Highland Stable. The Saddle is in a treasure chest that is buried in the ground, just behind where Malanya is located.
Check out the Interactive Map for a more precise location.