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Het (heterozygous) = one copy of the gene. Hom (homozygous) = two copies of the gene.

The genes that have to be homozygous recessive to affect a horse's appearance are: flaxen (ff), which lightens the manes and tails of chestnut horses; Satin (sasa), which gives a shimmer to the coat like what is seen in Akhal Teke horses; Mushroom (mumu), a closed gene derived from a real one found in British Shetland Ponies that lightens red coats; and Chinchilla (chnchn) which kills red pigment.

Some genes are complete dominant genes, which means that it takes only one copy to affect the horse's appearance and two copies (homozygous) won't look different. Rabicano (Rb) is one example. Silver (Z) on black based horses is another.

Other genes are incomplete dominants, which means that two copies change the appearance more than one does. Cream is an example of this. Two copies of cream have a greater lightening effect than one, so that we get Cremellos, Perlinos, and Smokey Creams when chestnuts, bays, and blacks have two copies of cream, and Palominos, Buckskins, and Smokey Blacks when they have one.

I just realized, working on this explanation, that thanks to fairly recent genetic discoveries, the number of complete dominant color genes in horses has been reduced by 2--Agouti now has 4 known alleles and Dun has 3! Thanks, Ammit for keeping the game up to date.