Glee: Kurt and Blaine sing Baby, It's Cold Outside. Purchase the album on itunes adopteesofcolor.org is excited that Chris Colfer (Kurt Hummel), whose plot-line. Like most holiday episodes, last night's (Dec. 7) "Glee" was heavy on the warm and fuzzies -- so much so that Grinch-like Sue Sylvester cracked. Lyrics to "Baby, It's Cold Outside" song by Glee Cast: I really can't stay But, baby, it's cold outside I've got to go away But, baby, it's cold outside Th. GLEE - Baby, It's Cold Outside (Full Performance) HD Season 2, Episode 10 - "A Very Glee Christmas". Baby, It's Cold Outside from Neptune's Daughter is featured in A Very Glee Christmas, the tenth episode of Season Two. It is sung at Dalton by Blaine and Kurt.