Rankin/Bass stop-motion features are recognizable by their visual style of doll-like characters with spheroid body parts, and ubiquitous powdery snow using an animation technique called “Animagic.” Often, traditional cel animation scenes of falling snow would be projected over the action to create the effect of a snowfall.
More productions, in similar style/era, are mentioned here....
http://en.wikipedia.org/wiki/Rankin/Bass_Productions
What I never realized, until read the credits at the end, was that the animation was done in Japan.
I remember the first time I saw it...two years after it premiered. I remember bawling uncontrollably at the very end when Santa called out “Merry Christmas!” I have no idea why.