For this post I have excluded all easier colours such as black, white, grey and a couple others.
Bay: A horse is brown in colour and has black points
Roan: A roan coloured horse is a horse with white hairs speckled throughout any one of the colours chestnut, bay, brown or black for its coat.
Piebald: A piebald horse is a horse which has black and white patches on its coat.
Skewbald: A skewbald horse is a horse which has brown and white patches on its coat.
Spotted horses: There are actually different types of spotted horses. Three are listed here: Leopard-spots are spots of any colour on a light coloured coat background. Blanket-spots are spots of any colour on a white rump. Snowflake-spots are white spots on a coat of any main colour.
Palomino: Some people say that the palomino is a breed when actually it is a colour. The coat colour is golden and the mane and tail colour is very light, almost white.
Odd-coloured: Odd coloured horses are horses that do not fit into any colour category.
Here are the majority of the colours listed:
Grey
Palomino
Bay
Black
Brown
Roan (Any type)
Liver-Chestnut
Dun
Piebald
Skewbald
Flea-bitten
Dapple-grey
Spotted (All types)
Odd-coloured
Here are some face marks listed:
Star
Stripe
Blaze
Interrupted stripe
White face
White muzzle
White lips
Snip
Here are some leg markings listed:
Erimine
Sock
Stocking
And finally, some hoof colours listed:
Striped
Blue/black
Please note that white is not actually a horse colour, it is a lack of pigmentation.