I think 'The Night Before Christmas' made me think that because it's the name of one of the reindeer.
That song would be Rudolph, the Red-Nosed Reindeer
that you are thinking of...
"You know Dasher and Dancer and Prancer and Vixen
Comet and Cupid and Donner and Blitzen"...
'The Night Before Christmas' is a book which children have read to them on Christmas Eve, quite a tradition in some families.
It's a poem A Visit from St Nicholas
by Clement Clarke Moore, an American professor of Oriental and Greek Literature in New York. It's often called "(Twas) The Night Before Christmas" because of its first line.
The reindeer Rudolph was created as a marketing device in 1939 for Montgomery Ward, an American retailer; the author's brother-in-law turned it into a song Rudolph, the Red-Nosed Reindeer
and the rest is history.