"a pinch; a sharp bite," 1540s, from nip (v.). Meaning "a chill in the weather" is from 1610s, probably so called for its effect on vegetation. Nip and tuck "a close thing" is recorded from 1832, perhaps from sailing or tailoring.
nip (v.)
"to pinch sharply; to bite suddenly," late 14c., related to Middle Low German nipen "to nip, to pinch," German nippen, Middle Dutch nipen "to pinch," Dutch nijpen, Old Norse hnippa "to prod," but the exact evolution of the stem is obscure. Related: Nipped; nipping. To nip (something) in the bud in the figurative sense is first recorded c. 1600.
nip (n.1)
"small measure of spirits," 1796, shortening of nipperkin (1670s) "quantity of liquor of a half pint or less," possibly of Dutch or Low German origin (compare German Nipp "sip, taste") and related to nip (v.). Reinforced by nip (n.2) on notion of "fragment or bit pinched off" (c. 1600).