Breeding is possibly the most important aspect of the game. It allow you obtain better horses by combining different pedigrees. You unlock breeding by wining the 16 mile race, or by having a GIII horse. In the beginning of the game you have only two different pedigrees, which is not enough to win every race. By using breeding, you can combine two pedigrees to obtain a better horse. When you breed a horse, he will inherit the traits of his parents. A horse can have a maximum of five traits, although only four of the five can be upgraded. The traits in the colt (male young horse) are combined adding the traits of the mare (female horse) to the end of the traits of the stallion (male horse). All the horses that you can have are stallions (buying or breeding), so you must bring your horse to another ranch to breed. If you breed a horse of pedigree A with a mare of pedigree B (both pure pedigree, not a bred horse) the colt will have four or three traits. The colt will have three traits if the stallion's last trait is the same as the mare's first one; in this case, that trait will be merged in an upgraded one. For example if you breed a stallion Phyton (strength +20, stamina +50) with a mare Hefty (stamina +50, gate +20) the colt will be Phyton or Hefty and will have (strength +20, stamina +100, gate +20). So if the colt is Hefty, he will have +20 strength and +50 stamina more than the a normal Hefty (same process for Phyton). A horse can only have five traits and if you breed a horse and the result would be six traits, the first one on the left will be dropped.
All horses get older at the same time no matter when they born. At the start of a new year (Month 7), all the horses age 1 year. This can affect the lifespan of your horse. If you breed a horse and he grows up on year 6 month 12, you lose a entire year of training because in year 7 month 1 he will be 2 years old. The best month of the year for breeding a horse is month 7, because it will grow up in the first month of the next year. The requirement to be able to participle in a classical tri crown is to have a 3 year old GI horse (4 years old GI horse for the dyrt tri crown). If you don't want to win races with a colt, then it does not matter when you breed him and it is advised that you do it as soon as possible to get the 3rd generation foals sooner. It is important to train the 3rd generation foal to the maximum stats possible, because the 4th generation will have better base stats and it will reduce the time that you need to train the new horse. The base stats of the horses are calculated based on the stats of the male parent and a random factor. It means that if you save the game before the colt grow up and then reload it, even if the pedigree of the horse is the same you will have a different result. So you can also use save and load to get a better horse of the same pedigree.