"Well, they certainly seem to be having a good time out there, Sprocket. Yep, I like it when they have a good time."
Also counts as a bit of a Tear Jerker, since this was one of the last things Jim ever did with these characters. It's almost like a dad looking in on his kids one last time.
Gonzo trying to convince the Turkey to leave the farm before he becomes Christmas dinner
The reason why Statler and Waldorf randomly pop up in the farmhouse? They're friends with Fozzie's mom and they visit her every Christmas!
Emily Bear's conclusion that the Muppets may be "weirdos, but they're nice weirdos."
The Swedish Chef being comforted by Big Bird's innocent offer of friendship and deciding that Christmas dinner will be "shredded wheat and cranberry sauce."
Robin the Frog and the Fraggles.
And the pebble.
While the Christmas carol singing sequence is heartwarming in itself, hearing Statler and Waldorf (of all people!) singing one of the carols is just adorable. (This is sadly lessened since this portion is cut out of some editions of the special.)
Specifically, they sing "I Heard The Bells on Christmas Day," a song about how being cynical on Christmas is easy, but being optimistic will make you happy and give you peace. Granted, it's really a bonus for the parents who know the rest of the song, but it's a heartwarming bonus. Even Statler and Waldorf can see the point in having Christmas spirit.
Doc offering to look for Miss Piggy when she's lost in the snowstorm, and explaining why;
Kermit: But you've never even met Miss Piggy!
Doc: Well, we never met any of you until a little while ago, and now we're friends. See, Sprocky and I were gonna spend Christmas alone, but this is better!