Talk with Strauss and go to Emerald Ranch to see Chick Matthews. Save the game at this point to have chance to try again if you fail. Take the map from Chick Matthews, then go to St Denis by train from Emerald Ranch. Find a buggy and start watching video. After taking the horse, ride it to Emerald Ranch and complete Chick Matthews treasure mission so then you are able to take the horse to stable. You can see which missions I completed at the end of the video.
The reason using Chick Matthew mission to get the horse is not to be followed by the law in Blackwater. Otherwise getting the horse will be almost impossible.
I wanted to play the whole game with a female tiger striped mustang horse. This is why I checked its sex in the video. :)
I hope you enjoy the video.