In the "A Very Goofy Christmas" segment, there are lawn flamingos dressed up for the holidays. They are based on the flamingos from "The Carnival of the Animals" segment in Fantasia 2000 (1999), which was in production at the same time as "Mickey's Once Upon a Christmas".
The department store Minnie works at, in the segment "Mickey & Minnie's Gift of the Magi", is named "Mortimer's". Mortimer is the name Walt Disney originally intended to give to Mickey Mouse. (Minnie's boss at the department store is Mortimer Mouse, a character who first appeared in the cartoon Mickey's Rival (1936).)
In the segment "Mickey & Minnie's Gift of the Magi", the Dixieland jazz band at the charity toy drive is made up of firefighters and named the Firehouse 5. This is a nod to the Firehouse Five Plus Two, a seven-piece Dixieland jazz band founded in 1949 and consisting of Disney animation staff (including lead animators Ward Kimball and Frank Thomas, two of Disney's famed Nine Old Men).