Hm, I think my setup is basic: Alt Diffuse > Hair > ColorRamp, and then each color outputs to a Noise nose. Then a Clouds node off the input of the ColorRamp. (And Diffuse_Color is set to 0.)

I'm liking the actual output; I'm just not seeing quite the variation I would expect.

Maybe my colour use is wrong? My Alternate_Diffuse colour is white. On the Hair node, I have Root_Color as black, Tip_Color as white, and specular as gray. (My minimal understanding of nodes suggests that both root and tip should be white when used with a ColorRamp, but that's not what my screenshot of your shader shows....) The Clouds node has Sky_Color as white and Clour_Color as black. All the desired hair colours are in the ColorRamp.

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Hardware: AMD Ryzen 9 3900X/MSI MAG570 Tomahawk X570/Zotac Geforce GTX 1650 Super 4GB/32GB OLOy RAM

Software: Windows 10 Professional/Poser Pro 11/Photoshop/Postworkshop 3