Could also be connected with "biting chill", "nippy":
bitter
O.E. biter, akin to bitan "bite," from P.Gmc. *bitras, from PIE base *bheid- "to split" (see fissure). Meaning moved in prehistoric times from "biting" to "acrid-tasting." Transferred to state of mind and to words in O.E. Bittersweet is 14c. in literal and figurative senses; bitters, so called for its taste, is from 1713. Phrase to the bitter end is attested from 1849.
http://www.etymonline.com/index.php?search=bi...nip (v.)
"to pinch sharply, to bite," 1393, related to M.L.G. nipen "to nip," Du. nijpen, but the exact evolution of the stem is obscure. The noun is attested from 1551. Nipper "small boy" (1859) was originally (1535) a pickpocket who "pinched" other people's property. To nip (something) in the bud in the fig. sense is first recorded 1606. Nip and tuck "a close thing" is recorded from 1832, perhaps from sailing or tailoring. Nippy in ref. to a "biting" chill in the air is first recorded 1898.
http://www.etymonline.com/index.php?search=ni...