Raising the bond Arthur has with his Horses in Red Dead Redemption 2 is more that just a fun little gimmick that developer Rockstar Games added to increase the immersion in their game. It serves a real purpose, and can help you greatly during the game if you invest time to raise it properly.
Each of the four Bond levels with your horse offer increased health and stamina for the animal, but at the same time, they also increase the distance from which your Horse can hear your whistle. It also affects your Horse’s demeanor, and a higher level ensures that it is less likely to flee during combat and leave you stranded without your arsenal.
Furthermore, at bond levels 2 and 3, you can even unlock advanced maneuvers that you can perform with your Horse such as drifting and sharp turns, that allow for greater mobility when traversing the landscape.
All you have to do to increase your bond with your Horse is to:
Ride your horse often: Riding you horse is the most common way of steadily increasing the bond.
Feed it occasionally: On top of restoring health and stamina, feeding helps build the bond quicker between you and the horse.
Interact with it: Brushing, Patting and Calming your Horse down are all great ways of quickly increasing the bond.