Rudolph the Red-Nosed Reindeer

Yes, this is the one you wanted to watch. From Wikipedia: 

Rudolph the Red-Nosed Reindeer is a Christmas television special produced in stop motion animation by Rankin/Bass Productions and currently distributed by DreamWorks Classics. It first aired Sunday, December 6, 1964, on the NBC television network in the United States, and was sponsored by General Electric under the umbrella title of The General Electric Fantasy Hour. The special was based on the Johnny Marks song "Rudolph the Red-Nosed Reindeer" which was itself based on the 1939 poem Rudolph the Red-Nosed Reindeer written by Marks' brother-in-law, Robert L. May.