In The Legend of Zelda: Tears of the Kingdom (TotK), you can catch horses by sneaking up to them from behind and mounting with the A-Button. Horses can then be parked at Stables and Mini Stables. You can catch any wild horse.
Horse Locations in Zelda Tears of the Kingdom
Horses are found in Central Hyrule > Hyrule Field > Passeri Greenbelt. It’s the field directly south of Lookout Landing, the first town you visit on the surface-level map. Exit Lookout Landing through the south gate and keep heading south until you see horses in the field.
How to Catch Horses
Sneak up to a Horse from behind. Press the Left Stick to crouch and tilt the left stick forward slowly to approach from behind. Horses often show up in groups. Try to stay out of all their sight, if they get spooked the will run away. Just wait until they have their back turned to you before you get close.
When you are within arm’s reach of a horse you will get a button prompt popup to press to mount it.
How to Ride Horses
Press A-Button to gallop, pull Left Stick down to stop, and press L-Button to soothe the horse when it gets irritated.
How Register a Horse at Stables
After catching a Horse, you must still register it at a stable to unlock it permanently. Simply ride to any Stable, marked by a horse icon on the map. Talk to the receptionist and click the dialogue “Register Horse”. You can dismount your horse near the receptionist or click ZR+A to talk to him while on horseback. The registration screen shows the stats of your horse and how strong of a bond you have with it. You can also give it a name.
Once a horse is registered, you can take it out at any other stable worldwide. You don’t have to go back to the stable where you first registered it. It will be available at any other stable too.
How to Tame a Horse
To tame your horse and increase the bond with it, pet it often with the L-Button. You will see some pink hearts around the horses head when the bond increased. You can just ride around for a few minutes and spam this button repeatedly. This will make the horse more obedient. You can view the bond at the stable after registering a horse.
If your horse pulls in a different direction than you want it to go, pet it with the L-Button and gently pull it in the desired direction. It will become more obedient over time. You can also unlock saddles, hardnesses and other horse-improvements by collecting Pony Points at stables. You receive these every time you talk to the receptionist at a newly discovered stable, and when you pay Rupees to sleep there. At the ledger inside any stable you can redeem Pony Points for these rewards.
How to Call Horse
If your horse is nearby you can press the Down-Button to whistle, which calls your horse. This won’t work if the horse is too far away.
That’s all there is to know about horses in Zelda TotK. For everything else needed for 100% Completion refer to Zelda Tears of the Kingdom Wiki & Strategy Guide.