In 1812, American author Washington

In 1812, American author Washington Irving refers to St. Nicholas as "— riding over the tops of the trees, in that self-same wagon wherein he brings his yearly presents to children" in the revised version of A Complete History of New York written under the pseudonym Diedrich Knickerbocker. Yet no mention is made of what propels the wagon. So where did the story of flying reindeer originate?