I love Nat King Cole's 1953 hit recording, but, thanks to boinx12 on YouTube, I've learned there are earlier versions, including the original audio recording below with an added duet of sorts voiced by the composer, Mel Tormé.
Mel Tormé didn't write a verse for his Christmas song until the 1960s, so Nat King Cole never recorded a version that included it.
Here's Mel singing the verse, followed by Nat's original recording, made at the WMCA Studios in New York City on June 14, 1946, but not released until 1989 on the Rhino album "Billboard Greatest Christmas Hits 1935-1954."
It features Nat on piano, Oscar Moore on guitar and Johnny Miller on bass.
The first released version was recorded the same year, with strings added, and again in 1953 (partly to correct the mistakenly sung "reindeers" heard in this version).