There are several solutions to get the hair to follow gravity independently from the head rotation.
Probably a simple and effective one would consist in having the hair not parented to the head, so that it is not influenced by its rotation, but then using a transform constraint to get the hair to follow the head translation. Optionally you could even sneak just a little bit of rotation influence.
A second option could be to disable "inherit rotation" for the hair bone. This one comes with the drawback that scale and rotations would not influence the hair the same way anymore.
A third option could be to apply gravity to the hair using physics.
