Every horse is born with a "base" color to his coat, either Red (e) or Black (E). Each horse carries two genes for base coat color (EE, Ee, ee, eE).  The Red gene is always recessive to the Black (dominant) gene.  Red horses (chestnuts and shades of chestnuts) are known to be homozygous for Red, because the chestnut gene is recessive, and therefore requires two copies of the Red gene to show red as the base coat color.

Gray is NOT a base coat color.  Think of it as if this were a human - we are not born gray, we just turn it as we age.  We have our base hair color  (blonde, brown, black) and then Old Man Age shows up and we turn gray.  Therefore, a horse that is homozygous or heterozygous for Red or Black can also be gray.

Black is a dominant base coat color.  Black can be either heterozygous (Ee, eE) or homozygous (EE).  Heterozygous blacks can produce horses that are red or black in base coat color.  This means, the horse carries one Black gene and one Red gene.  Since Black is dominant over Red, the horse appears with a black base coat color (black, bay, brown).  When a heterozygous Black horse is bred to a Red horse, he can produce a Red horse.  Two Heterozygous blacks can also produce a Red, if each passes on their red gene. This is why you can breed a bay to a bay and still get a chestnut.

A homozygous Black can only produce black or shades thereof (black, bay, brown).

Remarkable is a Homozygous black, meaning there was no Red detected in his DNA. He can be assumed to be homozygous for black pigment (EE). It cannot have red foals, regardless of the color of the mare. The basic color of the horse will be black, bay, or brown, but depending on genes at other color loci, the horse may be buckskin, zebra dun (this I would like to see!), grulla, perlino, gray, white or any of these colors with the white hair patterns tobiano, overo, roan or appaloosa.

Being a Gray, he will pass the graying on to approximately 50% of his foals. All offspring however will have the base colors as mentioned above.