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Kishimoto's reply was that he saw ninjas as being"mysterious" or something, so in his character design he madeKakashi wear a mask, but he didn't do that with othercharacters because it's too difficult to get their expressions downwhen you can't see their entire face.
Keeping this in view, why does Kakashi Hatake wear a mask?
So he wanted to protect Kakashi by making himwear a mask every time they got out of their houselike that no one would know how his face looked like. Than afterSakumo died Kakashi felt ashamed of his father, so hedecided to keep wearing the mask like that noonewould know he was Sakumo's kid.
Beside above, why does zabuza wear a mask?
It's not exactly a mask,he covers himself with acloth because he is a rogue ninja and loves to remain like one andI guess he doesn't want to reveal his identity.
To be clear, his colour is 'Grey' and not White.In an anime or a manga, a character's hair representshis/her personality. So, saying that Kakashi's hair colouris white would change his whole personality. Characters mayalso have grey hair to emphasize a modest, self-lessnature.