True
The first time reindeer were associated with Santa Claus was in the poem “Old Stanteclaus With Much Delight,” which was published in 1821 in New York, two years before the poem “A Visit from St. Nicholas.”
In the first poem, Santa only has one reindeer pulling his sleigh. In the second poem, we get the full eight-member team, featuring Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donder and Blitzen.