The War Horse was one of the bonus items for those who pre-ordered their copy of the Red Dead Redemption 2. Now that the game is released, many of you are also probably wondering how you actually get it. Well wonder no longer...

Unlike what you might be thinking, your War Horse isn't actually available from the start of your game. Instead, you'll need to wait until Chapter 2 and have first completed the "Americans at Rest" mission. Following that, you'll be eligible to take on the mission "Exit Pursued by a Bruised Ego" from Hosea Matthews at camp.
Hosea wants your help to sell his Shire horse and asks you to ride it into Valentine town with him. Do that and take the horse to the Amos Levi Blacksmith & Farrier stable. Head inside the stable mounted on the horse and a mission cut-scene should occur.
Following that you'll then be able to purchase various horses from the stable, one of which is Ardennes, a grey War Horse. However because you've pre-ordered the game it will be free. So simply select that horse and then begin the bonding process with it.
That's it, you now have your bonus War Horse, Ardennes.