Horse Color Genetics:
​The Base Color Genes
In short: the E gene tells a horse to be red or black. The A gene determines if black will be changed into bay, but has little to no effect on red.
The Importance of Base Color Genes

There are three different possible Base Colors in horses - red, bay or black. Most horses are one of these colors. Additionally, one of these three colors, along with white (or the lack of color),  is used to create all other possible colors. The Special Color Genes work by altering whatever base color your horse would have had without it. Thus, every horse has a Base Color of red, bay or black, even if that horse is not actually one of those colors. 

This means that even if your horse is not red, bay or black, in order to know what color babies it could produce, you have to know which of these three base colors it would have been if it had not had one of the Special Color Genes turned on.
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NOTE: By the way, in horses we call red either Chestnut or Sorrel. For the most part, Chestnut and Sorrel are interchangeable terms, both referring to the same color (some people like to use Sorrel to refer to brighter, more orange-red horses and Chestnut to refer to darker red horses, but most use them both to refer to any red colored horse at all. To make matters simpler, we will use the term "Chestnut" here to refer to all red horses. ​
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Base Color Basics

Unfortunately, nature didn't make understanding the base colors easy - it made them complicated. Instead of there being one gene which determines if a horse's base color is red, bay or black, there are two: the (E) Gene and the (A) Gene. The (E) gene determines if the horse produces primarily red or black pigment. The (A) gene takes any black body hairs and either leaves them alone (a) or dilutes them a bit so that they look lighter (A) - thus creating a bay. (The (A) gene  leaves the mane, tail and legs alone. That is why most bay horses have brown body colors but still have black mane, tail and legs.)
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To understand how Base Color is decided, we have to look at both the (E) and the (A) gene.
The E Gene

The E Gene has two versions:  Red and Black.  (To make things easier to write about, we call the Red version of the E gene "e" and the black version of the E gene "E".) Black is dominant to Red.  Thus, if a horse has even one black gene (EE or Ee) it will be black or bay. A horse is only a red horse if it has two (e) genes and no (E) gene (ee).
THEREFORE:
  • A horse with two red E genes  (ee) has a chestnut base color. 
  • A horse with two black E genes (EE) has either a black or bay base color.
  • A horse with one red and one black E gene (Ee) has either a black or bay base color.
The A Gene

The A gene can turn a Black horse into Bay (by bringing red into the otherwise black body hairs and lightening these dark hairs to brown). 

The A gene also has two versions. The dominant one (A) restricts black hairs only to the points (legs, main and tail). Basically, it takes any black hairs growing on the horse's body and changes them by making them lighter. It leaves the legs, mane and tail black. Thus, turning what would have been a black horse into a bay - some shade of brown with a black mane, tail and legs. 

​The recessive version of this gene (a) doesn't restrict the black hairs at all, thus not changing much of anything. So, if a horse is EE or Ee (black) it doesn't change anything. The horse stays black. And if the horse is ee (chestnut) it also doesn't change anything. The horse stays red.

In short, the E gene decides if the horse is going to be red or black. The A gene decides if it will change black to bay, but has little to no effect on red.
FOR EXAMPLE:
  • The version of the (A) gene which doesn't restrict black at all (allowing black hairs over the whole horse's body) creates a black horse. We call this "a".
  • The version of the (A) gene which restricts black only to the "points" (mane, tail and legs), allows black points but lightens the hairs over the rest of the body, creating a bay horse. We call this "A".
  • A chestnut horse is not as strongly effected by the A gene, since it doesn't have much in the way of black hairs anyway. In a chestnut horse, the A gene only effects which shade of red the horse turns out to be.
THEREFORE:
  • A horse with two red E genes  (ee) has a chestnut base color no matter what A genes it has. It could have (AA) ​ or (Aa) or (aa)
  • A horse with two black E genes (EE)  or one red gene and one black gene (Ee) and two recessive A genes (aa) is a black horse
  • A horse with one red and one black E gene (Ee) and either one of each A gene  (Aa) or two black A genes (AA) is a bay horse.
Possible Genetic Combination of Chestnut, Black and Bay horses:

Black horses could be either:
  • (EE) ​and (aa)
  • (Ee) and (aa) ​
Bay horses could be either:
  • (Ee) and  (Aa)
  • (Ee) and (AA) 
  • (EE) and  (Aa)
  • (EE) and (AA) 
Chestnut horses could be either:
  • (ee) and (AA) 
  • (ee) and  (Aa) 
  • (ee) and (aa)
Still Confused? Use these steps to determine the base color of any horse...
1. Look at the horse's E genes. Is either of them the dominant, Black E gene (E)?
  • ​​​if no = horse is a chestnut, no matter what the A genes are (EE) 
  • if yes = horse is either black or bay, depending upon the A genes. ​​(Ee) or (EE) 
2. Look at the horse's A genes. Is either of them the dominant, Bay gene (A)?
  • if no = horse is black. (Ee) or (EE) ​and (aa) 
  • if yes = horse is bay. (Ee) or (EE) ​and (AA) or (Aa)