keep one's hair

Chocolate Factoryにまた慣用句らしき表現が出て来ました。
...'I simply wouldn't feel comfortable if I didn't have that little wedge of gum to chew on every moment of the day, I really wouldn't. My mother says it's not ladylike and it looks ugly to see a girl's jaws going up and down like mine do all the time, but I don't agree. And who's she to criticize, anyway, because if you ask me, I'd say that her jaws are going up and down almost as much as mine are just from yelling at me every minute of the day.'
"'Now, Viotel,' Mrs. Beauregarde said from a far corner of the room where she was standing on the piano to avoid being trampled by the mob.
"'All right, Mother, keep your hair on!' Miss Beauregarde shouted. 'And now,' she went on, turning to the reporters again,...
"keep your hair on" を辞書で調べます。
・Wiktionary: (idiomatic, UK, colloquial) To stay calm; to be patient.: All right, all right, just keep your hair on, mate.
・Cambridge English Dictionary: said to tell someone to stop being so angry or upset: Keep your hair on! Your car isn't badly damaged!
"keep your hair on" を調べているとEnglish Language & Usageというサイトにこの表現の由来に関する次ぎのような記事がありました。
I have Googled and read something about keep your shirt on was the original expression and came from the days when ordinary man had two shirts and he had to take off his precious shirt before getting in a fight. ( First recorded in the USA in George W. Harris's 1854 book Spirit of the Times: 'I say, you durned ash cats, just keep yer shirts on, will ye?')
Keep your hair on was some sort of humorous development of this, but I still don't get how you are going to lose your hair if you get angry, not that all expressions have to make sense but I find it peculiar. Is it connected with the phrase let your hair down? The phrase comes from the same time period when women had to wear their hair pinned up on the head in public. They were only allowed to let their hair down to hang naturally when alone, either when bathing or at bedtime. The phrase means merely to relax and to go easy.
"keep your hair on" の由来は定かではありませんが、"keep your shirt on" とペアで覚えると良いかも。