What colors does a horse have?

The basic horse colors are black, bay, wild bay, brown and chestnut (sorrel).
The main modifiers of these colors are the dilution genes dun, creme, silver, champagne, pearl/barlink. Combinations of dilution genes can act in concert to produce additional colors.

For every basic coat color each dilution gene modifies that color to a new color (exceptions are
heterozygous creme with black and chestnut with silver where the dilution allele doesn't act on the base coat color.

The coat modifiers roan, rabicano, gray, brindle (rare).

There are also shading modifiers like sooty and pangare. that are poorly understood. which change the shade and depth of the base coat color.

The numbers of colors and their various shades is considerable.

This does not include spotting genes that produce appaploosa, tobiano, overo, sabino, etc.