Difference between Let one’s hair down and Put one’s hair up

let one’s hair down—(also: let one’s back hair down) throw off restraint in one’s behavior:

• Those who are doomed to a life of formality look forward to the week-end when they can let their hair down.

put one’s hair up—assume adult responsibilities:

• Lively young thing, I recall—but she’ll have put her hair up by now.

Note: The expression does not correlate in meaning with the phrase lift someone’s hair—(U.S. hist.) scalp a person:

• They [Indians] wouldn’t hesitate to lift the hair of any lone white man.