Final answer:
The genotypes for horse hair color with incomplete dominance are BB for brown, ww for white, and Bw for palomino, showing the principle of incomplete dominance.
Step-by-step explanation:
In horses, the genotypes for hair color that display incomplete dominance are as follows: homozygous dominant brown hair is represented by the genotype BB, homozygous recessive white hair is represented by the genotype ww, and the heterozygous palomino hair is represented by the genotype Bw. In this scenario, B is the allele for brown hair, and w is the allele for white hair. The palomino phenotype, being heterozygous, shows a tannish-yellow color which is intermediate between the homozygous dominant brown and the homozygous recessive white phenotypes, illustrating the principle of incomplete dominance where the heterozygote has a distinct phenotype.