Old English carian, cearian "be anxious or solicitous; grieve; feel concern or interest," from Proto-Germanic *karo- "lament," hence "grief, care" (source also of Old Saxon karon "to lament, to care, to sorrow, complain," Old High German charon "complain, lament," Gothic karon "be anxious"), said to be from PIE root *gar- "cry out, call, scream" (source also of Irish gairm "shout, cry, call;" see garrulous).
If so, the prehistoric sense development is from "cry" to "lamentation" to "grief." A different sense evolution is represented in related Dutch karig "scanty, frugal," German karg "stingy, scanty." It is not considered to be related to Latin cura. Positive senses, such as "have an inclination" (1550s); "have fondness for" (1520s) seem to have developed later as mirrors to the earlier negative ones.
To not care as a negative dismissal is attested from mid-13c. Phrase couldn't care less is from 1946; could care less in the same sense (with an understood negative) is from 1955. Care also has figured since 1580s in many "similies of indifference" in the form don't care a _____, with the blank filled by fig, pin, button, cent, straw, rush, point, farthing, snap, etc., etc. Related: Cared; caring.
Old English hær "hair, a hair," from Proto-Germanic *hēran (source also of Old Saxon, Old Norse, Old High German har, Old Frisian her, Dutch and German haar "hair"), perhaps from PIE *ghers- "to stand out, to bristle, rise to a point" (source also of Lithuanian šerys "bristle;" see horror).
Spelling influenced by Old Norse har and Old English haire "haircloth," from Old French haire, from Frankish *harja or some other Germanic source (see above). Hair-dye is from 1803. To let one's hair down "become familiar" is first recorded 1850. Homeopathic phrase hair of the dog (that bit you), remedy from the same thing that caused the malady, especially a drink on the morning after a debauch, 1540s in English, is in Pliny.
Old English caru, cearu "sorrow, anxiety, grief," also "burdens of mind; serious mental attention," in late Old English also "concern, anxiety caused by apprehension of evil or the weight of many burdens," from Proto-Germanic *karō "lament; grief, care" (source also of Old Saxon kara "sorrow;" Old High German chara "wail, lament;" Gothic kara "sorrow, trouble, care;" German Karfreitag "Good Friday;" see care (v.)).
The meaning "charge, oversight, attention or heed with a view to safety or protection" is attested from c. 1400; this is the sense in care of in addressing (1840). The meaning "object or matter of concern" is from 1580s. To take care of "take in hand, do" is from 1580s; take care "be careful" also is from 1580s.
The primary sense is that of inward grief, and the word is not connected, either in sense or form, with L. cura, care, of which the primary sense is pains or trouble bestowed upon something. [Century Dictionary]
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 longhair, 1893, "cat with long hair," from long (adj.) + hair (n.). As "intellectual," especially in musical tastes, "devotee of classical music," 1920 (late 19c. long hair was noted as a characteristic of classical musicians, perhaps inspired by the famous locks of Liszt). Sense of "hippie" attested from 1969. The adjective long-haired is attested from mid-15c.
Forty years ago, a music teacher who was not born abroad and who did not wear long hair was regarded with suspicion. He was spurious—not the real thing. On the face of it he could not be a good musician. [W. Francis Gates, in "The Music Student," vol. i, no. 3, October 1915]