Instructions
Changing your Horse
The easiest way to get a new horse is to buy one. From nearly any general store you can purchase a horse "voucher" ranging in quality from sickly and useless to blue-ribbon material. Simply use this voucher from your kit using the Back button, whistle, and you have a new horse.
Once your reach Armadillo and complete a couple of missions you'll be asked to help break a wild horse. This mechanic requires you to lasso a horse, hold the lasso while you approach the angry animal and then mount and ride it for several seconds without getting bucked off. Once you've tamed the beast, you are free to ride around per usual. If you lasso a wild horse like this and then hitch it, it will become your new steed.
Finally, you can steal horses. Life in the Old West just ain't authentic without some horse thievery, so go ahead and hop on any old saddled horse and ride it to a hitch to capture it for your own.