You may have noticed that simply holding the shift button, (Except for when you're following someone) won't increase your horse's speed.
How Sprint works? How to Increase Horse's Speed?
In PC version of the RDR1 holding the shift button won't increase your horse's speed, you need to double push it to gain a small speed increase.
1. Double push Shift button for five times. You need to wait for three second between each double push.
2. Now hold the Shift button to keep your horse at the max speed. When your character bends a little bit, that's your cue that you are at the max speed.
*. You can only get to the max speed on the road.
How to disable Sticky Keys warning?
If you push the Shift button repeatedly on PC, you will get a warning message which you can disable easily.
1. Open Settings and go to Accessibility > Keyboard > Sticky keys.
2. Turn off "Keyboard shortcut for Sticky keys".
Enable Hold Shift to Sprint Option
If you don't want to have to deal with any of the problems above, you can simple change the way your horse gains the maximum speed.
1. Open Menu > Options > Keyboard.
2. Turn on the last option "Hold Shift to Sprint (On Vehicle)".
*. If you're having hard time with horse's stamina ending too fast, push W and then Shift for sprint and then let go of W whenever your horse is running out of stamina. Wait for horse's stamina to go up and press W to drain it again.