Just thinking out loud. Is it possible to use the texture paint to ‘dye’ hair particles? Would be awesome if we could… maybe we can already. 
You can have a texture effect the hair colour. Pretty much the same thing.
You can paint a texture UVmapped on mesh which can color hairs using same material.
But only location of hair’s root indicates its color not displayed in 3D View as it will be rendered.
That’s pretty cool, sure, BUT DOES ANYONE KNOW HOW TO PREVENT THE DARNED UV TEXTURE FROM AFFECTING THE HAIR COLOR (and possibly using a second texture for that) ??? (!!!)
Perhaps you’ll get a better response if you ask this in the support forums… and refrain from typing in caps with excessive punctuation.