I have dark blonde hair, green eyes, very fair pink skin and I can wear every shade of green. Same when my hair was light brown with a lot of red. Teal is O.K.
With the exception of really shimmery white hair like my mother had I really think skin tone and eyecolor are more important than hair color.
I bought as much as I could of Louis malachite this year. True green is hard to find. Also I collect malachite jewelry and it works with the clothes.
Red, which I also wear a lot and green can be hard to wear; I think most of us learn what works: the right color brings the compliments. When I had my colors done there were no surprises.