Hunt for the Giant Horse
Talk to Straia at the Mounted Archery Camp to start this quest.
Set this quest as the objective marker to get a general heading.
The recommended path is to curve around the ridge to the south before heading northwest to the Taobab Grassland. On this path, however, there are numerous Blue Bokoblin riders, as well as two Red-Maned Lynels. It is recommended to take out all the enemies beforehand to make for a much safer path. The Giant Horse has a much lower maximum speed than that of some of the other horses, so it is very risky to try to run away from the enemies in the area.
The Giant Horse can be found alongside a bunch of smaller horses and it is very easy to identify, given its large size. When approaching the horse, it is recommended that Link has level 3 stealth so that the horse does not run away. Alternatively, Link can reach the horse by paragliding down from one of the large trees, landing right on top of the horse. Furthermore, once Link mounts the horse, he will need to soothe it. This will take over two full wheels of Stamina. So you'll either need to have several Stamina Vessel upgrades, or have a Stamina generating elixir or meal that you can consume while soothing the horse.
Once you have the horse soothed, ride it back to Straia and talk to him to complete the quest. After he examines the horse, he will give Link a Silver Rupee. Link gets to keep the horse, so it is recommended that Link ride over to the nearby Highland Stable to register the horse.
You captured the giant horse in Taobab Grasslands.
Giant was an accurate description, to be sure. This beast could probably trample monsters with ease.
When you brought it back to Straia, he was very surprised.