(New Austin Walkthrough)
Exodus in America
When you gain control over John Marston after the opening video, walk through Armadillo Station and cross the street to the saloon. Enter the saloon and watch the cutscene that ensues. After the cutscene, follow Jake outside and then approach the Painted Quarter Horse hitched to the hitch post along the side of the saloon. Press the Y/Triangle button to mount the horse and start following Jake toward Fort Mercer.
Ride with Jake to Fort Mercer.
The horse controls in Red Dead Redemption are simple: use the Left Stick to direct the horse, hold the A/X button to trot, tap the A/X button to spur the horse and tap the RB/R1 button to slow the horse (hold the RB/R1 button to stop completely). When spurring the horse to increase your speed, keep an eye on the horse's stamina meter on the left side of the Mini Map. Continuing to spur the horse when its stamina is depleted will slow it down; continue spurring the horse thereafter and it will eventually buck you off. While traveling with an AI companion who is also on horseback, you can hold the A/X button to match their speed. Hold the A/X button to match Jake's speed as you follow him to Fort Mercer.
Once you've reached the place, touch the yellow marker outside to trigger a cutscene.