nose-dive n.

Middle English nose, from Old English nosu "the nose of the human head, the special organ of breathing and smelling," from Proto-Germanic *nuso- (source also of Old Norse nös, Old Frisian nose, Dutch neus, Old High German nasa, German Nase), from PIE root *nas- "nose."

Used of beaks or snouts of animals from mid-13c.; of any prominent or projecting part supposed to resemble a nose from late 14c. (nose cone in the space rocket sense is from 1949). Meaning "sense of smell" is from mid-14c. Meaning "odor, scent" is from 1894. In Middle English, to have one's spirit in one's nose was to "be impetuous or easily angered" (c. 1400).

Kiv, It could bee no other then his owne manne, that had thrust his nose so farre out of ioynte. ["Barnabe Riche His Farewell to Military Profession," 1581]

To pay through the nose "pay excessively" (1670s) seems to suggest bleeding. Many extended meanings are from the horse-racing sense of "length of a horse's nose," as a measure of distance between two finishers (1908). To turn up one's nose "show disdain, express scorn or contempt" is from 1818 (earlier hold up one's nose, 1570s); a similar notion is expressed in look down one's nose (1907). To say something is under (one's) nose "in plain view, directly in front of one" is from mid-15c. To be as plain as the nose on one's face "very easy to be seen or understood" is from 1590s.

1700, "a descent or plunge headfirst, a sudden attack or swoop," from dive (v.). Colloquial sense of "disreputable place of resort for drinking and vice" is  recorded in American English by 1871, perhaps because they typically were in basements, and going into one was both a literal and figurative "diving."