There are some exceptions: e.g., I've read you should always write "Douglas-fir" instead of "Douglas fir" because it's not actually a fir.
red-head scarf might suggest that the flairs at the end of the scarf are red, and that it just a normal scarf https://www.google.ca/search?safe=off&tbm=isch
where as a red head-scarf would be a red... head scarf. https://www.google.ca/search?q=head+scarf&tbm=isch
Dunno. Needs more context frankly.