Agouti refers to the A allele. In this case think homo Agouti is not really an adequate word to refer to that horse. She has 2 AtAt alleles (Which I love very much) which means that she will pass that to all of her offspring
You can see it on her hooves and in some of the spots:) I believe brindle is a type of somatic mutation so should be able to happen on any coat or breed theoretically