Do helmets stop bullets?

[Sneaksie]

In the game, hit in the head without helmet usually means death, while helmet saves its user. Note however, that helmet in inventory won't do anything - wear it first (drag and drop it on soldier's figure in inventory).
AFAIK, moving speed and equipment weight are independent values.

[Korsakov829]

Alright, so the helmet protects the wearer. I'm wondering though, what if a soldier is wearing a helmet and he gets shot just a little below it, like on the nose.

Do the caps and officer hats work like a regular helmet? A Panzerwaffe Cap looks as if it is only cloth, and will offer no protection.