For the Horse to unlock you need to find the three places on the map which are called Sites of Grace. As you move around the map you will find little brightening light that shines. You have to find three Sites of Grace. There is no specific way to find these sites. You just have to go around the map in order to find the sights of Grace. Make sure you find each location.
What you have to do when you find the location is you have to rest at each location point it will unlock the fast travel for you. You have to do this three times and many times at least when you actually encountered a character called Melina. Different places such as Stranded Graveyard, Church of Elleh, The First Step, Groveside Cave, and GateFront.
Melina is going to give you the ability to obtain a horse but she also going to give you the ability to do some upgrades. So the first time you encounter her she is going to grant you a Ring which is called Spectral Steed Whistle. This will allow you to summon up the horse which is a kind of spirit Horse which is called a Torrent. If your Spectral Steed dies you can summon it again but it will cost one Flask of Crimson Tears to do. Add this to your quick access menu because you going to use him a lot and also in combat.
When you encounter Melina she has the ability to upgrade during the time of conversation at that time you can upgrade in the level a menu where you can level up the characteristics needs. By changing any of these it will change the stats like Runes Held and Runes Needed.
The torrent is basically the Horse that increases the overall speed and can also double jump which will help you a lot while escaping the group of enemies or if you need to find the treasure above the ground. There are some points where you can perform a super jump. You can use torrent during combats.