Its only a primary means of recognition if you see the face. For instance, I would not expect to be forced to shave my facial hair so you can see my face uncovered. Anytime you've seen my face it has facial hair on it.
Anytime you've seen her face, she's had the veil.
I've never seen your face ... but I expect I'd be able to see a hooked nose or a scar over your left eye or .... if you weren't wearing a disguise.