how can I teach my horse to pick up my hat and give it to me? You will need to have a trash can or large bag of treats that your horse loves. Keep an old hat in that can for several days so that the scent of the treats permeates it.
When you are ready to spend time with your horse in learning to pick up the hat have him in a stall or small area so that his attention can be focused on the hat and treats. Put the hat on the ground. If he puts his nose down to the the hat give him a treat as soon as he touch it. If he needs help in lowering his nose to the hat give him a treat and then when he is done eating it hold another treat lower towards the hat and let him get that one. Practice with this and have your hand with the treat lower each time you feed him until he does touch the hat.
Once he can touch the hat with his nose each time and you give him a treat hold off until he moves the hat to the side and then give him a treat. Practice this for a few times and then quit for several hours or till the next day.
The next day go ahead and practice once or twice what you have already done with him and the hat. When he does that well now is where you need to be really patient. Go ahead and hold a treat down near the hat. He will probably nudge the hat but hold off in giving the treat. He will nudge the hat again. Still hold off on the treat. The third time if he doesn't grab the hat go ahead and give him the treat when he nudges it. The reason we go ahead and reward him this time is so that we keep him interested and don't have him give up trying. Keep practicing this till he actually grabs the hat and then reward him. Do this several times and then again quit for awhile or till the next day.
This 3rd day practice again a few times of him grabbing the hat. After he is grabbing the hat consistently practice having him hold it longer till you reward him. If he drops it too soon then hold off on the treat till he grabs the hat again. Like what we did in day 2 go ahead and reward the treat on the 3rd try of picking up the hat even if he doesn't hold it long enough for you. Again this is so that we keep him interested. After he is holding the hat longer start bringing the treat closer to his shoulder which causes him to turn his head to you for when you are on his back. Practice this everyday or at least a few times a week. Eventually your horse will get proficient in grabbing the hat and turning his head to you so that you can grab it.