You might try it with some u-v-mathematics like in the second left iroquese in my gallery image.
But this is a trial and error game cause it seem that the u-v-coordinates are following the scalp cap and not the hair as such.

And you can combine the hair node with other, e.g. the HSV node. By a tip of Dimension3D I pushed the Hair node to the hue channel, anyway its the second channel of hsv, and set color to full red (255,0,0 RGB). This will make nice colorful effects, as seen in my gallery image.

But one shouldn't forget that the hair node is a lighting node, so the color effects are subject to change with changing of the main lights and their directions.

But for some specific colored streaks in the hair, I guess, you'r right. There must be given hair groups.