Paint is dominant, so if the mother is a homozygous paint then the baby will be too. In addition, recessive genes needs to be passed down from both the sire and the dam, so unless the mother has it in her genotype it will not appear in the foals phenotype. It will however be in the genotype, so that foal would have the possibility of passing down the trait.
Oh, and unless he carries a cream gene/dilute gene he will never produce a cremello or perlino foal.
I don't know much about dominance for horse colors and I'm not the best with genetics either.