From what I gather on the game info we know so far, there is a nice advantage built into the game. Let's say you are out in the wilderness, and your horse doesn't make it through a battle with a wild cougar.
In some games you might be stranded with a long walk ahead of you.
What Rockstar has done is put in a random horse that can be trained, it will be spawned every time (somewhere reasonably close) the player loses their horse.
Just train a new horse and you should be back in business, no money needed. Hope this helps.
That info was printed here along with lots of other horse info, etc. to get us even more excited for this game:
If your horse dies and you go more than a few minutes without a steed the game will present an opportunity to get one.