1. Map. Hold Start button to immediately access the map
2. Max Payne dive. While aiming press Jump and the direction, Arthur will perform dive in which you can't shoot, but combining it with dead eye allows you to mark targets before you exit the animation.
3. Toggle Run. If you tired of holding Run button you can change it to press Run button once, simply go to Settings -> Controls -> Accessibility and switch to Toggle to Run.
4. Shooting locks. Early in the game you won't have all the equipment Arthur will have later, and sometimes roaming around you can find locks that will require you a Lockbreaker, don't worry, just aim at the lock and shoot it.
5. Warning Shot. Some of the NPCs (witnesses or people you trying to rob) won't listen to Arthurs command to stop. In that case, while chasing down NPC, Aim your gun, press up on the D-Pad and shoot the bullet in the air. After one or more stop him again.
6. Horse bond. While on the horse press Left Stick, and Arthur will Calm/Talk/Pet with the horse.
7. Hitch your horse. You can hitch your horse to almost any tree in the world. Hitching the horse advances the bonding, so don't be lazy and love your trusty mount.
8. Camp. In open world hold down Y (Triangle) and you can craft/cook or set up the camp, without going through the horse inventory.
9. Keep the guns. If you equip guns you want while on the horse, the template will be auto saved, and every time you dismount the horse Arthur will bring selected guns with him.
10. Chain animations. When looting and there is a lot of items, Hold X (Square) to chain animations and pick up everything in the vicinity.
11. Chain animations 2. If you have cargo, when you hitch the horse Hold X (Square) to chain taking off cargo/person animation.
12. Feed the horse. You can feed the horse on the go, just slow down a little bit partner.
13. Tackle. Funny thing you can tackle by pressing B (Circle) button while on the horse.
14. Whistle. There is no practical need for this, but depending on how long you hold Up on the D-Pad, the longer you whistle.
15. Binoculars. Use binoculars to Study animals before killing them, there is always information about the best weapons to use. Also get your achievement/trophy for Studying every single animal. P.S. you can bring binoculars on the horse.
16. Lost hat. Your horse inventory will have last 3 hats stored for you.
17. Pick up new guns. If you swap your Repeater for a Shotgun, your horse will automatically store Repeater for later use.
18. Stow multiple dead animals. You can stow multiple pelts on your horse, small animals (birds, rabbits, etc.) can be placed on each sides of the horse.
19. Drink in the saloon. Every time you in the city, visit the saloon and order a drink, it will trigger the animation in which Stranger will tell you interesting things about the city, or will slip out information about the auction, or the house you might wanna rob.
20. Cinematic camera. If you place the marker on the map, and then turn the cinematic camera, all you have to do is set up the speed and let the horse do the rest of the ride. Enjoy beautiful landscape, switch angles by clicking the Right Stick and move Right Stick to move the camera.
If you know more tips right them down and I'll add them to the list.