No, it doesn’t have anything to do with a rooster—but it does have something to do with a horse. Type “origin of word cocktail” into your search engine and you may see a dictionary entry that explains the term cock-tailed originally described a horse with a docked (or clipped-short) tail, and “cock-tailed” became a sort of pejorative for racehorses without thoroughbred pedigrees—with mixed lineage, if you will. So the term may have come to be applied to alcoholic drinks that were similarly blended rather than pure spirits.
No, it doesn’t have anything to do with a rooster—but it does have something to do with a horse. Type “origin of word cocktail” into your search engine and you may see a dictionary entry that explains the term cock-tailed originally described a horse with a docked (or clipped-short) tail, and “cock-tailed” became a sort of pejorative for racehorses without thoroughbred pedigrees—with mixed lineage, if you will. So the term may have come to be applied to alcoholic drinks that were similarly blended rather than pure spirits.