I can't remember where I came across it (possibly Gowers' Plain Words), but I like the rule that you should hyphenate to avoid ambiguity but not otherwise. E.g. is "a red head scarf" a red scarf for the head or a scarf for red heads? From context, it should be obvious, but hyphenating "head scarf" would make it explicit. (Of course, you could always avoid the problem entirely by using "headscarf" instead.)

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.

If you need an hyphen to make clear what a "read head scarf" is, shouldn't you rewrite your sentence?

Well I don't know if this is right, but if I had to guess

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.