This traditional Christmas melody is usually called "The Huron Carol" or "The Indian Christmas Carol" or "'Twas in the Moon of Wintertime". A Jesuit missionary in Canada adapted an old 16th Century French tune into a Christmas Carol, adding words in the local Huron language which he taught to the Indians where he was based. This arrangement is for piano and we also have an Arrangement for Guitar by Glenn Jarrett.
If you have a different instrument here are a range of printable versions which should suit most instruments: Main, High, Bass, Clar, Horn, Sax and Viola. With each of these versions piano teachers can use the following Piano Accompaniment.