Colors in Horses
The horse is a prey animal. The most important purpose af a prey animal´s coat-color, is camouflage and that´s why wild horses, like other prey animals, all have the same color. The only living wild horse left, is the Przewalskihorse. 
If a foal with a different coatcolor, a mutation, was born in a herd of wild horses, it would most likely never survive. It would either be chased away by its herd for looking different and, or, it would be killed by predators, because it stood out from the herd. But for the more than 5000 years the horse has been domesticated, these color-mutations have not only been allowed to live, but many of them (once they were seen) specifically bred for, and that has resulted in the exuberance of coat-colors we see in horses today.
There are three basic colors in the horse´s color genes and they are Bay, Chestnut and Black. These three basecolors can be modified into a number of other colors, for example, if one of the basecolors is mixed with white hairs, the horse will be Grey or Roan. Other modifications dilute the basecolor and make it lighter.
The color of a foal, will be determined by one gene from its mother (dam) and one gene from its father (sire). Some genes are dominant, which means they will show if they are there (Phenotype), and others are recessive, which means they can be in the genes but not seen on the horse (genotype). For example, if a foal gets a bay gene from its father and a chestnut gene from its mother, that foal will be bay (the dominant color), but will be able to produce chestnut offspring. If the two genes from the parents are the same, the horse will be called homocygous, and if they are different, the horse will be called heterocygous.
Bay - Photo Credit: Wikipedia
Bay horses can be Red-bay, Blood-bay, Mahogany-bay and Dark-bay. A bay horse has black mane and tail.
Sorrel - Photo credit: Wikipedia
The Chestnut horse can be light (Sorrel) or dark (Liver Chestnut). Most have mane and tail in the same color as the body, but hey can have flaxen mane and tail also. Some people call these Palominos, which is wrong as they do not carry the Cream gene.
Black - Photo credit: Wikipedia
The black horse should have a deep, rich black color (apart from white markings) and the mane and tail should be black as well.
Grey - Photo credit: Wikipedia
The Grey horse has one of the basecolors mixed with white hairs, they are born black (or dark) and will turn grey and end up being white.
Roan - Photo credit: Wikipedia
The Roans also have one of the basecolors mixed with white hairs and are also born dark. They can turn lighter, but will never turn white like the greys. The gene for Roan is dominant and is lethal in double dose. This means that if two roans are crossed, one third of the offspring will be homocygous for Roan, but will perish in the early embryonic stage.
White - Photo credit: Australian Crabbet Arabians
A dominant white horse is born white. They can have dark spots on their skin, but the coat is white and the eyes are usually brown.The term Albino is often used, especially if the eys are blue, but this is not correct. A true albino (pure white coat, pink skin and red eyes) has never been seen in horses. The reason is thought to be that the gene is lethal in double dose, like the roan gene.
Tri-color - Photo credit: Wikipedia
There are many variations of broken colors in horses. White with one (or more) of all the above mentioned colors in many different patterns.
Spotted - Photo credit: Wikipedia
Dilutes:
In horses there are four different Dilution genes, that dilute or modify all the basic colors.
Grulla - Photo credit: The Glacier Ridge Ranch
D-series (Dun) - dilutes all the basecolors, but more on the body, neck and head than on the legs, mane and tail. The Blue Horse of the West, The Grulla, is a D-Dilute. D-dilutes have dorsal stripes.
Palomino - Photo credit: Wikipedia
C-series (the Cream gene) - dilutes chestnut and bay, but has little effect on black. Basically, the Cream-gene on a Chestnut will produce a Palomino, the Cream-gene on a Bay will produce a Buckskin; double Cream-gene on a Chestnut basecolor will produce a Cremello and double cream-gene on a Bay basecolor will produce a Perlino.
Buckskin - Photo credit: Wikipedia
The gene is dominant, which means if it doesn´t show, it´s not there! HOWEVER, because the effect of the gene is less noticable on Eumelanin, a grey or dark horse actually CAN carry the Cream gene and be able to produce a Palomino or a Buckskin. These horses are called Crypto Palominos.
Cremello - Photo credit: Wikipedia
Perlino - Photo credit: Wikipedia
S-series - Silver Dapple gene dilutes bays and blacks, but does not have a big effect on chestnuts. The dilution is most noticable on mane and tail.
Silver Dapple - photo credit: Wikipedia
Silver Dapple - Credit: Crystal Ridge farm
Silver Dapple - Credit: Miniatureequines
Ch-series (the Champagne-gene) dilutes skin, coat, mane, tail and eyecolor on ALL the basecolors. The gene is dominant. Horses with this gene usually have blue eyes at birth and the color changes to golden, amber or light brown as they grow older. The Ch-gene on a black basecolor will produce a Classic Champagne, the Ch-gene on a bay basecolor will produce an Amber Champagne and on a chestnut/sorrel basecolor, it will produce a Gold Champagne.
Gold Champagne - Photo credit: Eagle Ridge Farm
Sable Champagne - Photo Credit: ICHR
Amber Champagne - Photo Credit: ICHR
Classic Champagne - Photo Credit: ICHR
Top Photo credit:
The Foundation for the Preservation and Protection of the Przewalski Horse.