D-Horse is available from the very beginning of the Metal Gear Solid V or to be specific: from the Phantom Limbs mission.
Information about D-Horse and how to use its help
The main purpose of having a D-Horse is to allow you to move through the world faster. It is important especially if you have to follow the enemy convoy or get to the distant area in a short time. Moving faster will also allow you to complete some missions in a shorter time what may be important if you want to receive the S rank. Travelling on D-Horse allows you also to duck while sitting in saddle what may help you to avoid the enemy patrols. D-Horse is not very durable however it is not weak enough to die after the first bullet. Later on you may develop the various types of horse armors which will also provide it some extra protection.
Developing your relation with D-Horse is fairly easy since riding him is pretty much all you need to do. After getting to the half of the Bond bar you are going to unlock the new order which will force D-Horse to take a poop in a place where he stands. It is a surprisingly effective way of stopping the enemy vehicles, much more efficient than, for example, putting a basic cardboard box on the middle of the road.