Horsehair buttons seem to be as rare as hen's teeth. We have contacted many costume collections, none of which have any examples. We have found one 17th century museum garment that is reported to have horsehair buttons, but it is displayed in a manner that protects the item from light and does not permit close examination.
We are now working our way through button collecting sources. If you can share an image of a horsehair button, preferably from the 1700's, please contact us at Buttonworks1@gmail.com. We have a group of long-tailed horses willing to donate hair in return for extra treats!
Better yet, if you know of someone who reupholsters period furniture with plain black horsehair fabric, we only need about two square inches of scrap to recreate a period button.