Confused yet? Here's a quick glossary to help you use the right words.
Bay - a brown or reddish brown horse with black points. In horses, the points are the mane, the tail, the legs below the main joints and the tips of the ears.
A bay horse of unknown breeding
Chestnut - a red, orange, or deep yellow color. In the U.S. west this is called sorrel, and you will sometimes see chestnut/sorrel.
A medium chestnut Quarter Horse.
Mealy chestnut - a chestnut horse with lighter color around the muzzle and flanks. Confusingly, in parts of the midwest, people use chestnut for a regular chestnut and sorrel for a mealy.
This Icelandic mare is both mealy and flaxen, to save space. She is also a lighter and brighter shade than the Quarter Horse above.
Liver chestnut - a very dark chestnut horse. Some liver chestnuts are brown and a color not dissimilar to that of chocolate labradors is fairly common. Rarely, a liver chestnut can look completely black and I've also seen a spectacular color with a black body and flame-colored mane and tail, presumably caused by the flaxen gene.
This Tori stallion is a pretty moderate liver chestnut - I've seen darker. Image source: Rozpravka via Wikimedia Commons.
Black - just as it says, but black horses often have red through their manes and across their backs, especially in summer. This is sometimes called "summer black" or "fading black" - and is caused by the same mechanism that gives some people pretty highlights in summer.
Note the reddening in this Icelandic mare's mane, indicating that she is probably a "fading" black.
See how much darker this grade gelding is than the mare above.
Brown - generally used for either a very faded black or a very dark bay. True brown horses with no color variation across the points are extremely rare.
Seal bay or seal brown - a brown with lighter color around the muzzle and flanks. Caused by the same gene that gives mealy chestnuts.
This hunter shows the effect of the mealy gene on his nose. The greying also visible on his face is a sign of age - old horses get a bit grizzled around the face.
Grey - a horse that turns white with age. Grey horses are born whatever color they would have been without the grey gene and slowly fade to white. Usually they start to turn grey at puberty, but I've seen foals white at birth and once knew a horse that greyed so slowly he died of old age before reaching white.
This Icelandic mare has turned almost completely white.
Dappled Grey - a grey horse that has rings of darker hair on its coat.
Quarter Horse showing extensive dappling.
Fleabitten Grey - a grey horse that has flecks or specks of darker hair on its coat.
This Asil mare shows heavy fleabitten. Note that she shades to red whilst the dappled horse above appears more black. Image source: Alexander Kastler via Wikimedia Commons.
Interestingly, dappled grey horses are more likely to have a base of black or bay, whilst fleabittens seem more likely to have a base of chestnut.
White - white horses do exist, contrary to legend, but are very rare - the white gene does not always turn the horse completely white. Total albinism is unknown in horses and presumably lethal.
A rare dominant white. Source: Haase B, Brooks SA, Schlumbaum A, Azor PJ, Bailey E, et al. (2007) Allelic heterogeneity at the equine KIT locus in dominant white (W) horses. PLoS Genet 3(11): e195. doi:10.1371/journal.pgen.0030195
Palomino - a yellow or gold horse with a white mane and tail. Highly valued in the western show community.
Image source: Kiss Girl via Wikimedia Commons.
Buckskin - a yellow or gold horse with black points. Also highly valued in the western community.
The dappled patterning on this New Forest pony is fairly common with buckskins. Image source: Wikimedia Commons.
Cremello - a pale cream horse with light skin and blue eyes.
Perlino - a pale cream horse with light skin and blue eyes, differs from cremello in having slightly darker points.
This is either a cremello or a perlino - it's hard to tell which. The shine to the coat is a characteristic of this horse's breed - Akhal-Teke. Image source: Лена via Wikimedia Commons.
Dun - a light brown horse with black points. Dun horses are distinguished from buckskins by also having a very defined black stripe down their spine and many also have black stripes on their lower legs. (In England, however, all light brown, yellow, or gold horses with dark points are called dun, regardless of the presence or absence of a dorsal stripe).
This shot shows the dorsal stripe on a dun horse. Horses of other colors may have fading or indistinct stripes, but this is definitely a dun. Image source: Arsdelicata via Wikimedia Commons.
Dunskin - a yellow or gold horse with brown points and a brown dorsal stripe - these horses have both the gene that causes dun and the gene that causes buckskin.
Norwegian Fjords are classically dunskin. Note the two-toned mane, which is caused by the dorsal stripe being narrower than the base of the mane - called "frosting" in buckskin and dun horses. The leg stripes are not much darker than the surrounding hair.
Red dun - a red horse with a dark red dorsal stripe and stripes on the legs.
A red dun Icelandic, with the dorsal stripe clearly visible. This horse also has mane frosting, but it's not quite as spectacular as on the dunskin above. Source: Hansueli Krapf via Wikimedia Commons.
Dunalino - a light yellow horse with a dark yellow dorsal stripe and stripes on the legs. Called palomino duns in England.
Grulla/grullo - a dark grey horse with black points, dorsal stripe, and leg stripes. Called mouse dun or grey dun in England, and also occasionally blue dun. Traditionally gender-differentiated in the US (a grulla mare and a grullo stallion).
Image source: tiboudne62 via Wikimedia Commons.
Roan - a horse with dark and white hairs evenly mixed through its coat. In England, also used for a horse with roaning on the lower part of its body.
Red roan - red-brown body with white hairs mixed through the coat, black points.
Some roans have unevenness in the hair color, as shown by this red roan Quarter Horse. The dark spots on his hindquarters are called corning.
Strawberry roan - light red body with white hairs mixed through the coat, red or flaxen points. Sometimes called chestnut roan in the US.
A strawberry roan Belgian. Don't mind me, I'm only half dressed...
Blue roan - black body with white hairs mixed through the coat, black points.
A team of Dutch Drafts. Note that the one on the left has a frosted mane and thus may be dun as well as roan. Image source: Amanda Slater via Wikimedia Commons.
All roan horses have dark points.
Rabicano - white hairs across the flank and rump of the horse and in the base of the tail. Called "skunk tail" in England. Common in Thoroughbreds.
This is really extreme rabicano to show the effect. It's generally much more subtle - this is a purebred Arabian. Image source: Coreada via Wikimedia Commons.
I'll talk about terms for multi-colored horses tomorrow, because this has gotten long!