Should I even take it off?

Description:

I once asked a friend of mine if she would take of her scarf to stop a severe bleeding. She had to admit she did not know. - And later (probably a couple of months) on that there would be a bigger chance that she would rather use her sweatshirt to stop the bleeding. From what I have been taught from my friend is that when a muslim wears a scarf she may not showcase her hair to a male stranger. Even her brother in law is not allowed to watch her hair. But she may show her hair to her brother, father and uncles. Plus of course every woman who exists as long there is no male present of course. So I guess I am asking: Would you take of your scarf to save a life?