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 scyrte "skirt, tunic," from Proto-Germanic *skurtjon "a short garment" (source also of Old Norse skyrta, Swedish skjorta "skirt, kirtle;" Middle Dutch scorte, Dutch schort "apron;" Middle High German schurz, German Schurz "apron"), related to Old English scort, sceort "short," from PIE root *sker- (1) "to cut," on the notion of "a cut piece."
Formerly of the chief garment worn by both sexes, but in modern use long only of that for men; in reference to women's tops, reintroduced 1896. Bloody shirt, exposed as a symbol of outrage, is attested from 1580s. To give (someone) the shirt off one's back is from 1771. To lose one's shirt "suffer total financial loss" is from 1935. To keep one's shirt on "be patient" (1904) is from the notion of (not) stripping down for a fight.