In the movie industry, a white hat was someone in a western movie in which such a character would wear a white hat in contrast to the villain's black hat. Examples of such characters are Red Ryder, Tom Mix, and The Lone Ranger.
Rob Brydon riffed on this iconic use of the white hat in the TV series Director's Commentary when his character, director Peter De Lane, discussed making a 'good' character in a Western wear a black hat: "Can a good guy wear a black hat? Can a bad guy wear a white hat?"