Horse coat color is controlled on several different gene loci so
the idea of pure white or pure red is erroneous.
Red Color is controlled at the Extension locus and Non-red color
is controlled at the
Agouti locus. The genetics of a horse at the Extension locus
masks the genetics at the Agouti locus in some instances.
Any horse that is ee at the Extension locus is chestnut or
sorrel.
Any horse that is Ee or EE is not chestnut. The main available
alleles at this locus are a (black), A (bay) and At (brown/black
bay).
Note that there is no allele for White at either the Extension
locus or the Agouti locus.
There are two types of white, Dominant White (there is still a
debate on the exsistence of this allele and the original school of
thought was that only the Ww white foals were viable and a WW white
conceptus died during development) and Maximum expressed Sabino
which is SbSb at the
sabino site. Both these genes act as modifiers to the base coat
colors. So there really is no "pure".