1795; Figurative use by 1841. Hair perhaps in reference to the slight pressure required to activate it.

The difference between a hair-trigger and a common trigger is this—the hair-trigger, when set, lets off the cock by the slightest touch, whereas the common trigger requires a considerable degree of force, and consequently is longer in its operation. [Charles James, "Military Dictionary," London, 1802]

also hair-cut, 1887, "act of cutting the hair," from hair (n.) + cut (n.). As "style of wearing the hair," by 1890.

The Romans began to cut the hair about A.U.C. 454, when Ticinius Maenas introduced Barbers from Sicily. Then they began to cut, curl, and perfume it. The glass was consulted as now upon rising from the barber's chair. [Rev. Thomas Dudley Fosbroke, "Encyclopædia of Antiquities," London, 1825]

Related: Haircutter; haircutting.