Speed Racer is right. Genetics are the most important factor in determining hair growth. Nutrition is the second most important. If the horse is missing any essential amino acids it won't grow. If other components are missing, it won't be healthy, and will break easily.
I have an appaloosa, and boy do I ever wish that they had thicker longer manes but my best advice and what has helped my appaloosa is braid it ! And also DO NOT brush/comb it , it will only cause hairloss just comb thru with your fingers ! And if you see any split ends just cut them !:)