Horses are an essential part of Red Dead Redemption 2 (RDR2) as not only will they act as the main mode of transport in the game, they have also revamped the player-horse dynamic. You might also want to see Horse Tack, Horse Grooming and Horse Bonding.
Horses in RDR2
No More Unicorns
In the original Red Dead Redemption, horses were seen solely as a mode of transport, and more importantly, expendable. This lack of connection would often result in the death of a whole lot of horses that could be easily replaced by another, or miraculously revived by infinitely activating the 'Horse Deed' in the player's inventory after purchasing it. Red Dead Redemption 2 scraps all of this and completely changes the way you think about, and interact with not only your horse, but horses in general.
Horses in RDR2 no longer respawn; once a horse is dead, it dies for good. This changes the approach players take when dealing with horses as the player would need to either purchase a new one from a Stable, wrangle one in the wild, or steal one, every time their stallion dies. However, it is also possible to own several horses at once, and keep them in a Stable, which allows the player to access any one of them at any given time. That being said, if the player finds themselves in a firefight with their horse and want to avoid losing it, they can command their trusty stead to flee the scene, to return to the Stable.
Happy Horse, Happy Life (Grooming)
RDR2 has also added a new mechanic into the game in the form of a horse-player bond. Players are able to build a bond with the horse by taking care of it properly, which comes with a number of benefits, most of which being buffs to the horse. Properly maintaining a horse will improve it's speed, stamina, health, and its calmness under tense situations. Horses with strong bonds can also hear the player's whistle from further away, and will learn new tricks and ways to maneuver.
Grooming is the main way to build a bond with your horse. This includes feeding it regularly, brushing it, keeping it clean, and interacting with it positively. This also unlocks customizable options for the horse, some purely aesthetic, while others are also functional.
On the other hand, if players fail to build a bond and properly tend to their horses, the opposite happens, and they may even kick the player down if you try to mount them from behind; this is also true for horses that are stolen from other people that may have built strong bonds with them.
See Horse Bonding for more details.
Red Dead Redemption 2 contains a lot of customization throughout, and that doesn't stop at the horses. While the player won't necessarily be able to dye their horse pink or turquoise (remember realism is another key component), players will be able to customize majority of the Horse Tack, and even style the hair on the mane and tail.
Apart from buying and stealing them, horses can also be acquired by finding and wrangling them in the wild. All that is needed is a Lasso, and a horse that is fast enough to catch up to a wild horse. Once the target is located, players can use their lasso to subdue the desired horse, and subsequently mount it. This will trigger a mini-game in which the player must balance in the middle and avoid getting thrown off. Doing this for long enough will break the horse, and it'll belong to the player until it dies. The player can then use the horse as their own, store them or sell them at a Stable.
Horse Breeds in RDR2
There are a total of 19 horse breeds in Red Dead Redemption 2, consisting of different tiers of horses, with different focuses. For example, some are quicker and stronger, while others are better for transporting animal carcasses and cargo. This allows players to strategize when it comes to owning horses, rather than just opting for the speedsters or the colorful ones. Horses can be categorized into classes, then further into breeds: