late 13c., "close-fitting cap," from Old French coife "skull-cap, cap worn under a helmet, headgear" (12c., Modern French coiffe), from Late Latin coifa "a cap, hood" (source of Italian cuffia, Spanish cofia, escofia), of West Germanic origin (compare Old High German kupphia, Middle High German kupfe "cap"). As "light cap of lace worn by women," mid-15c.
mid-15c., coifen, "to cover with a cap," from Old French coifier, from Old French coife (see coif (n.)); sense of "to arrange the hair" is attested in English from 1835. Related: Coifed; coifing.
"hair-dresser," 1817, a French word in English "affected by fashionable or artistic hair-dressers, and their patrons" [OED], from French coiffeur "hairdresser," agent noun from coiffer "to dress hair," from Old French coife, originally, "inner part of the helmet" (see coif (n.)). A woman hairdresser would be properly a coiffeuse.
Prussian spiked helmet, 1875, from German Pickelhaube, from pickel "(ice)pick, pickaxe" + haube "hood, bonnet." But the German word is attested 17c., long before the helmet type came into use, and originally meant simply "helmet;" Palmer ("Folk-Etymology") reports a German theory (Andresen) that it is a folk-etymology formation: "as if from Pickel and haube, a cap or coif[;] more correctly written Biekelhaube, [it] is for Beckelhaube, a word most probably derived from becken, a basin."