"While Shepherds Watched Their Flocks by Night" is a composed carol, words by Nahum Tate, first appeared in "Tate and Brady's Supplement," 1700. (I can't check this out, but the reference appears in several books.
Dr. Ralph Dunstan said "Probably no Christmas Carol of Hymn ever written has so many settings as "While Shepherds...". www.hymnsandcarolsofchristmas.com
The setting by Handel is my favorite, but I'm sure everybody has their own..