That song was written by John Frederick Coots and Haven Gillespie in 1934. They were both popular songwriters of the time, and they wrote several Christmas songs together, including "You're a Mean One, Mr. Grinch" and "Put One Foot in Front of the Other." The song "We Wish You a Merry Christmas" has been a popular holiday tune ever since it was first published, and it is still sung and performed every year during the Christmas season.