Hello,
If someone 'goes white in the face', then they are very scared and their face becomes paler. In frightening situations, adrenaline is released which then prepares you for a 'flight or flight' response to the situation. A white face is caused because there is reduced blood flow to the surface of the body.
Blood is pumped to other areas of the body instead such as arms, legs, shoulders, brain, eyes, ears and nose.