There are two primary sources - the first is from horses that have been slaughtered for other reasons. or which have died of natural causes. Bow makers generally use horse hair that has been taken from the slaughterhouse because of the quantity they need.
The second, of course, is hair harvested from live horses, most often from the tail (Mane hair is finer, though, and some craft people prefer it). When I was a kid, the lesson barn sold one pony's spectacular mane to somebody who was restoring a carousel horse with a natural tail. He looked silly while it grew back, but it certainly didn't hurt him.
Hair from horses that grew up in cold climates is considered superior.