Hidden Genes can be purchased via Stable Upgrades in the Pro Shop for Pro Coins. They can be purchased separately, or in a bulk Stablewide option. They are also included within the Forever Pro Package. They can also be purchased in a bulk stablewide option in the Pro Shop, which will give you this for all horses you currently own and all horses you ever own. These will also appear on the horse's Genetics page. Hidden genes give you ratings for the specialty genes and the stat genes. The stat genes will appear in a table below the Genotype.
These ratings will include the colors Cream, Roan, Dun, and Silver; the color markings BendOr, Birdcatcher, Brindle, Masque, Lace, Frosting, Badger, Mustache, Stocking, Overo, Rabicano, Sabino, and Tobiano; and the genes for Male Probability, Female Influence, and Heritage. The stat genes portion includes a rating for each of the 6 main stats.
These ratings work the same way as normal ratings do. The only one that is more confusing is Heritage, since it is actually broken into two parts. Heritage has four gene pairs, so it looks like Hh Hh Hh Hh. Heritage I is simply the first two pairs, and Heritage II is the second two pairs. They combine together for the same function, but are broken down into two pairs for ease of understanding (rating a 4-pair gene would get very confusing).