It requires pointed breeding and the ability to genetically test to be 100% sure you have done so, but it is perfectly possible. The only reason that some breeds like Frisians (who are almost universally black) and the like haven't had their recessive color genes (red, in this case) bred out is because not every horse is tested and not every horse is bred to a Frisian.

It's not even totally impossible in Randland, as you have a genetic test for channeling...the a'dam. Cull anyone and everyone who can wear or wield it and you'd do a very good job of removing the gene. This, of course, does not account for the Wheel's Will, but I'm speaking strictly from a scientific standpoint, not including magical influences.