Part of the Breath of the Wild Expansion Pass content is a quest to find Ancient Horse Gear. This page explains how to find it and use it on a horse.
How to Get the Expansion Pass
You can purchase the Expansion Pass for Breath of the Wild via the "Downloadable Content" option on the title screen, or from the System menu (press + then press R until you reach the System menu).
Make sure to save your game and go to the Nintendo Switch Home Screen to download the latest version of Breath of the Wild. You can press + or - while the cursor is on the Breath of the Wild icon in your Home Screen menu, then go to Software Update to get the latest version.
Learn Where the Gear is Hidden
Go to Highland Stable, near Ka'o Makagh Shrine, and read the book on the table inside. This will update your Adventure Log with information about where to find the Ancient Horse Gear.
Find the Ancient Saddle
The Ancient Saddle can be found at Malanya Spring. This spring is southeast of the Ka'o Makagh Shrine. You can follow the road west from Highland Stable, then turn left at the fork, and go to the end of the road to find the spring.
The Ancient Saddle is in a treasure chest partly behind the spring. Use Magnesis to pull it out of the ground.
Find the Ancient Bridle
The Ancient Bridle can be found under the large cherry blossom tree on Satori Mountain. Read the Mogg Latan Shrine page for information on how to find Satori Mountain. The tree is north of the shrine.
The Ancient Bridle is in a treasure chest under the tree. Use Magnesis to pull it out of the ground.
How to Equip the Ancient Horse Gear on a Horse
You can only change the gear of a horse that you found and tamed in the wild.
You can only change a horse's gear if you have registered it at a stable and you have a maximum bond with it. Raise your bond with the horse by soothing it after it jumps over an obstacle, or by soothing it after it calms down after disobeying. You can check your bond by registering the horse at a stable and choosing "Take horse" to see the list of horses that you have registered.
After you have a max bond with a registered horse, take it out of the stable. Talk to one of the stable workers (not the person behind the counter, but one of the people in stable gear). If you talked to the right person, he or she will check your bond with that horse, then offer to change the horse's gear.
What the Ancient Bridle Does
The Ancient Bridle gives your horse the maximum number of spurs, which are displayed on the screen when your horse is galloping. Spurs are used to give your horse a burst of speed when galloping.
How to Use the Ancient Saddle to Summon your Horse Anywhere
After you put the Ancient Saddle on a horse (see above for instructions), take that horse out of the stable. Then you can press the down button of the directional pad to whistle. If there is enough room in front of you, your horse will materialize there. There are some locations where horses can't be summoned. You can't summon your horse if it is boarded in a stable, so make sure to take it out of a stable first.