Horse Color Genetics: Base Coat Colors

All horse colors are derived from red (chestnut/sorrel). Surprised? It is really that simple. All horses either have dominant or recessive of these two colors. The status of what color they are and which are domiannt or recessive is shown with what I call a color genome sequence. The length of this sequence can be long or short, depending on how simple the color is.
In a horse that is red, all the color genes in it are recessive. Red is really the base to all coat colors, even black. Red is not really a color gene, every single horse has it. To define red, any redish or brown horse with the same color mane, or slightly darker or lighter. Red is the same as chestnut and sorrel in the genetics world.
If you can pretend that for a minute that horses are buckets of paint, please do. A red horse is like a white bucket of paint. A black gene can come in and completely change the color, diluting the color until it is gray.
Keeping in mind that red is the base for every color, how does a black horse get black? If every horse is red, a black horse inherited a dominant black gene. This made it black. It doesn't matter whether it got two dominant black genes or one, it will still be black.
Here is a red horse; a red horse has recessive genes for every other color except maybe for bay (I'll get to that in a minute).

Because every horse is really a form of red, there is not code for red; every horse has a small code for what it's genetic color is (what it can pass on, whether each color is homozygous or heterozygous, etc.). Some more complicated color patterns are a little longer, but no matter the color, the amount of black is always shown.
Black is represented with an E. Capitol E is dominant, lowercase e is recessive. If a horse's color code is ee, then it is not black. Simple. The chestnut horse above is ee, I can tell by looking at it. If a horse is Ee or EE, then it will be black. The horse below looks like a Fresian, so it is probably EE. All Fresians are black, which you can conclude that all Fresians are dominant homozygous (so you know that two black horses make a black).

If the black horse above had not received any dominant genes (you could think of dominant and recessive like positive or negative), then it would be chestnut.

Now for a more complicated color! Is your brain hurting yet?
Bay is another base coat. It is a red horse with a black mane and tail, and black points. When I say points, it basically means the outermost edges (mane, tail, legs, the tips of the ears).

So genetically, how does this work out?

This is another gene. Remember, every horse is red until you do something to it. The bay is a red horse who has inherited either one or two black genes (it doesn't matter whether there is one or two). But it can't only be black genes, because then it would be black! A bay horse also inherits one or two bay genes (again, it doesn't matter). This pushes the black to the outermost edges.

Here is where it gets even more confusing. Some red horses carry one or two bay genes inside them and you wouldn't know, but if there is no black to push out then it won't be apparent from the outside. The representation for the bay gene is A. AA homozygous dominant, Aa heterozygous, and aa for homozygous recessive. 

Black is a dominant gene; this means that if they have only one dominant E gene, it will take effect. However, bay is not, because it is incomplete by itself. 

*As a side note, usually when horse breeders refer to their homozygous stallion, they are advertising the dominant gene, not the recessive. They do that because people like to know what they are getting :).