Appearances in Christmas specials
Kermit appears early on in the first Sesame Street Christmas special, Christmas Eve on Sesame Street. When Big Bird becomes worried that Santa Claus will not be able to deliver presents to anyone after Oscar the Grouch points out the physical impossibility of a man like Santa coming down skinny chimneys, Kermit tries to help him solve the mystery. Along with Grover, Kermit inquires various kids for their theories on how Santa comes down a chimney. Kermit is later shown reading some of the theories to Big Bird.
In Elmo Saves Christmas, Kermit makes a brief appearance in his famous role as a news reporter. He appears in a news flash that interrupts a TV showing of It's a Wonderful Life to report about everyone doing their Christmas shopping on December 25th because it is going to be Christmas again tomorrow (due to Elmo having wished that every day was Christmas). An Anything Muppet comes up to him, saying that his kid wants a microphone like the one Kermit is using. Kermit initially refuses to sell his microphone, but begins to relent when the Anything Muppet offers a hundred dollars.
In John Denver and the Muppets: A Christmas Together, the first Christmas television special featuring the cast of The Muppet Show, Kermit and the gang join singer John Denver for a show in which they all sing Christmas songs. At one point, Kermit and Denver reminisce about past Christmases with their friends and families, and sing the song "The Christmas Wish".
In A Muppet Family Christmas, Kermit and his Muppet Show friends spend Christmas at Fozzie's mother's farmhouse, eventually joined by many of his friends from Sesame Street as well. Over the course of the special, Kermit becomes worried that Miss Piggy will not be able to make it to the farmhouse due to the snowstorm currently going on. He and his nephew Robin also pay a visit to the Fraggles and learn about their own holiday tradition.
The Muppet Christmas Carol marked the Muppets' first Christmas production following Jim Henson's death, and as such, was the first Christmas production in which Kermit was performed by Steve Whitmire. In this adaptation of Charles Dickens' A Christmas Carol, Kermit portrays the role of Bob Cratchit.
Kermit plays a very prominent role in the Muppets' first feature-length made-for-TV movie, It's a Very Merry Muppet Christmas Movie. In this adaptation of It's a Wonderful Life, Kermit and the gang put on a special Christmas show in an attempt to save the Muppet theater from being taken over by banker Rachel Bitterman. Unfortunately, they ultimately fail to bring the money to Ms. Bitterman on time, and Kermit feels that he's let everyone down. When an angel named Daniel shows up to help him, Kermit thinks the Muppets would be better off if he had never been born. Daniel then transports Kermit to a world where he never existed, and he sees how miserable his friends' lives would be without him. After seeing this, Kermit promptly wishes to be brought back to the world he knows.
In A Muppets Christmas: Letters to Santa, the first new Christmas special starring the Muppets after being acquired by The Walt Disney Company in 2004, Kermit and Fozzie join Gonzo in traveling to the North Pole to bring three lost Christmas letters to Santa.
As the infant version of Kermit is one of the main characters of Muppet Babies, he appears prominently in the 2018 series' Christmas episodes, "A Very Muppet Babies Christmas" and "Summer's Super Fabulous Holiday Surprise".
Other Henson Christmas specials
Prior to any of the Sesame Street or Muppets Christmas specials, Kermit's first appearance in a Christmas special was in Emmet Otter's Jug-Band Christmas, based on the storybook of the same name. Kermit appears at the beginning and end of the special to provide opening and closing narration. When the special was aired on ABC in the 1980s, a few scenes were cut down and replaced with Kermit providing new narration to fill in the gaps in the story. As a result of Disney having obtained ownership of the character in 2004, Kermit's scenes were cut entirely from the special's subsequent DVD releases. However, they were reinstated when the special was aired on the Disney-owned network ABC Family in 2015, as well as on the 40th Anniversary Edition DVD release two years later.
In The Christmas Toy, Kermit, dressed as Santa Claus, appears at the beginning and end of the special to serve as the story's narrator, much like his role in Emmet Otter's Jug-Band Christmas before. As with Emmet Otter, Disney's 2004 acquisition of the character resulted in Kermit's scenes being cut from the DVD releases as well as the Hub Network's broadcasts of the special.
Kermit once again played the role of the narrator for Mr. Willowby's Christmas Tree, based on Robert Barry's 1963 storybook. This time, Kermit also appears onscreen after each commercial break, and is seen attending Mr. Willowby's Christmas party at the end of the special.
Non-Muppet Christmas productions
Years before Disney officially acquired the Muppets, Kermit had a brief cameo in The Disney Christmas Special.
Along with his fellow Muppets, Kermit appeared as a guest star in Holiday Greetings from the Ed Sullivan Show to promote the release of The Muppet Christmas Carol.
Kermit and his fellow Muppets made appearances in Christmas in Rockefeller Center in 2008, 2009, and 2012.
In 2017, Kermit appeared as a special guest in a segment from A Very Pentatonix Christmas. In the segment, Kermit is framed for the theft of Pentatonix's Christmas presents. It turns out that the presents were actually stolen by his criminal doppelganger, Constantine from Muppets Most Wanted. This segment notably marked the first Christmas production in which Kermit was performed by his current Muppeteer, Matt Vogel, who also performed as Constantine (Vogel was assisted by Mike Quinn, who would puppeteer one of the two characters while he performed the other between shots).