Answer:
The foal resulting from breeding a buckskin horse and a pinto could have many coat color and pattern possibilities. It would depend on the base color making up the buckskin, and on which pattern(s) the pinto had. It will also depend on the base color of the pinto horse, since pinto is only one part of the coloration.
Since the base color of the pinto isn't given, there is no way to truly map out the color possibilities. From the buckskin, you have a fifty percent chance of getting the cream gene, which is about the only think that can be narrowed down. The horse might be homozygous for black or agouti, meaning you would always have a bay-based horse. All of the other factors have to be considered in.
Basically, you might get black, you might get bay, or buckskin, half might be pinto. The rest of this vast layout of possibilities depends on the exact genetic makeup of both parents.