The attachment of reindeer to Santa Claus was first done by William Gilley in "A New-Year's Present to the Little Ones from Five to Twelve." Written in 1821, the book includes one poem which contains the line: "Old Santeclaus with much delight / His reindeer drives this frosty night..." Don Foster says that this addition to the poem "was new, entirely original, quirky, and quintessentially American" (262). While this version only included one reindeer, the Christmas historian Charles Jones said, "Moore knew how to multiply; he was perfectly capable of turning one deer into eight..." (Foster 263). Foster argues, however, that Gilley must have gotten the idea from someone, and that he probably got the idea from Henry Livingston Jr. A scholar himself, Henry Livingston Jr. was very interested in northern cultures, and would have been made privy to the ideas of "Lapland reindeers, and of the Norse god Thor, whose chariot was said to have been pulled by air-borne 'He-Goats.' By combining the pipe-smoking Dutchman of the Hudson Valley with the reindeer of Lapland and the flying goats of Norwegian mythology, our Christmas poet created an American original. Santa has traveled by reindeer ever since" (Foster 263-264). Joe Nickell, on the other hand, argues that because Gilley wrote his piece in 1821 and "A Visit from St. Nicholas" was published in 1823 that the idea of eight reindeer must have formed between these two dates. This supports the case that Moore wrote the poem, as he claimed to have written "A Visit from St. Nicholas" in 1822. Nickell also states that Clement Clarke Moore "not only lived in New York, but he was a frequent customer, friend, and neighbor of Gilley" (8).
Foster, Don. "Author Unknown: On the Trail of Anonymous." New York: Henry Holt and Co., 2000.
Nickell, Joe. "The Case of the Christmas Poem." Manuscripts 54.4 (2002): 293-308.