Definitely not a Dun - in the third picture, you can see enough of the baby's back and backside to see that there is no dorsal stripe.
Horse babies display a form of cryptic coloration where the foals are usually born a lot lighter than the color they will be as adults. As
@Shezadandy said, the foal fuzz usually starts shedding out around the eyes, so the mature color tends to show up there first, gradually spreading down the face and neck. If the horse standing behind the foal in the third picture is the sister you spoke of, I think he'll probably wind up looking a lot like her. His mane and tail are pretty light right now, but the mane clearly has dark roots; they will probably get a lot darker as the hair gets longer . . . though it's possible that Silver could be in play here.
As
@Overo Mare pointed out, for the baby to be a Buckskin, one parent would have to be either a cream or dun dilution, and Chestnut and Black are not dilute colors. The few colored areas the mare has don't really appear to be diluted, either, though I suppose she
might be a Smoky Black (a genetic Black with the Cream gene), in which case, that seems likely to be the foal's color, too.