"Blue Christmas" by Rory Flanagan (Damian McGinty)
"Santa Baby" by Santana Lopez
"Christmas Wrapping" by Brittany Pierce
"All I Want For Christmas Is You" by Mercedes Jones
"River" by Rachel Berry
"Santa Claus Is Coming to Town" by Puck (Mark), Finn Hudson (Cory), and unknown character (Samuel Larsen)
"Extraordinary Merry Christmas" by Rachel Berry and Blaine Anderson
"Do You Hear What I Hear?" by Harmony (Lindsay Pearce) and unknown character (Alex Newell)
"Do They Know It's Christmas?" by New Directions
"Let It Snow" by Kurt Hummel and Blaine Anderson
"Little Drummer Boy" by Artie Abrams
"Christmas Eve With You" by Emma Pillsbury and Will Schuester
The tracklist for the Christmas songs is
link if you want to check.