Fastest and most powerful horse for the off road in RDR1 is the Dark Horse.
1. Get your Honor Level as low as possible. You can achieve this by getting on a good spot and killing people in the city.
2. Call your horse, instead of your normal horse, a black horse will appear with a little message on top left corner of the screen.
*. Dark Horse does not lose speed in off-road and going through the brushes.
*. He has white face, black body, and visible scars on his legs.