If you go to the general store, you can purchase horses by buying a deed for them. Instead of buying the deed, check the info, and it will give you a description of the horse's appearance. You can compare this information with horses you break to help determine the horse breed.
Another good way to determine a horse's breed and quality is to break and ride them just a few seconds. You should be able to instantly tell the difference between a 1-star, 2-star, and 3-star horse. The stamina will deplete much quicker the lower the quality, and the horse itself will not run as fast. Physically you can also tell a difference. If you can see any ribs or bones, the horse is low quality, while thicker more muscular horses are the 3-star ones. You can get the 3-star Pearl from the "Bonnie" mission very early in the game. The Hungarian Half-bred is found in Mexico and is an off-white color. The Standardbred Pinto is all black and can be found in Mexico. Other horse breeds that can be found throughout the game are American Standardbred, Ardennais, Cleaveland Bay, Dutch Warmblood, Friesian, Highland Chestnut, Kentucky Saddler, Lusitano, Painted Quarter Horse, Painted Standardbred, Quarter Horse, Tersk, Tobiano Pinto, Turkmen, War Horse, and Welsh Mountain.