If all of the offspring have roan coats-white hairs mixed into a base coat of red-what can be said about the red and white alleles for coat color?

The alleles for red and white coat color are co-dominant.

Explanation:

Co-dominance is the condition when none of the allele of a gene is dominant. The heterozygous genotype exhibits traits of both alleles.

In the given example, the offspring have roan coat color in which white hairs are mixed into a base coat of red. Since both the alleles are expressed in heterozygous offspring, the alleles for red and white coat colors are co-dominant over each other.