If I understand it correctly, the female knight is wearing a "grandhelm", which is a helm that's so big it's worn over another, smaller, helm. This way, you can make it to the melee with your head safe, then drop the big helm (that gets in the way of seeing pretty much everything), and fight in your more normal helm.
Still no excuse to wear such a constricting helm while travelling. Maybe she really doesn't want her face to be seen, because she has a birthmark or a wanted poster or something.
@ash32121 - historically, helmets are one of the first types of armor used. The head is that vulnerable, and it's easier to make than body armor.