In Arabians a parent has to be black (non homozygous), chestnut or grey to get a Chestnut. Being you said one parent was Straight Egyptian(SE) and black is where thoes white hairs are comming from. This tends to be more common in SE Arabs. I have a SE Chesnut Sabino who is white flecked, mother was a bay but dad was black till about 5 then started going grey.
Arabian color genes are different from the rest of the horse world, white markings, rabicino, or sabino markings are not caused by "pinto genes". Arabians do not carry that gene at all.
But hope this helps a bit. And his polish lines show through...his body especially.
Proudly owned by 2 amazing Arabian geldings.