You're almost correct, "The Leprechaun's Christmas Gold", "Pinocchio's Christmas", "The Story of the First Christmas Snow", and "Nestor, The Long-Eared Christmas Donkey" all air on AMC during the Christmas (since all post-1974 Rankin/Bass specials are owned by Warner Bros) alongside Rudolph's Shiny New Year and "A Year Without A Santa Claus". Glad to know the lesser-known Rankin/Bass Christmas Specials still air on television.

I also loved "Nestor, the Long-Eared Christmas Donkey" because of how perfectly executed they handled talking animals set during The Nativity. To this day, I can't think of any other fictional donkey that looked as adorable as Nestor. Fun Fact, the special is actually the voice acting debut of Brenda Vaccaro who voiced Tilly (best-known as Bunnie Bravo from Johnny Bravo and Scruple from the Smurfs).