breeding brown horses
Where brown horse have the brown agouti allele then breeding brown horses together would also result in brown, black or chestnut foals, but not bay ones, as follows below. If Gower is also right about the affect of the alleles on shades, the chestnut foals would be expected to be liver and standard chestnut, rather than the chestnut and sorrel which might be more likely for a dilution model.
If both the parents are heterozygous at the extension locus then there is a 1 in 4 (25%) chance of the foal being chestnut. If one or both of the parents are of genotype E+E+ then only black or brown foals can result. Black foals will only be produced if both parents are of genotype AtAa at the agouti locus.
The following demonstrates what happens when two brown horses are bred together which are both heterozygous at both loci:
There is a 9:3:4 ratio of brown: black : chestnut, or put another there is just over 56% chance of a brown foal from any particular breeding. (The agouti allele in the chestnut horses is irrelevant to the phenotype since there is no black pigment to distribute, either uniformly or in the points.)