"Shakespearean Santa" - the story of Rudolf in the style of Shakespeare.
"Waiting for Christmas" - a short monologues and scene for 4 or more actors about finding the true meaning of Christmas... hint... the answer is not shopping.
"The First Star of Night" monologue about the true meaning of Christmas
"Ebony Scrooge" modern Christmas Carol play and monologues from the play "My Punishment," "Greed Killed Her," and "The Spirit of Christmas Indigestion."
"Black Friday Selfie" monologue and scene for 2 actors - comedy about the dangers of Christmas sales
Christmas Improv and Games
A great children's play that can be done as a musical is "Songs of the Pioneers" which as an old frontier theme that can be done as a holiday play. It's a good script for celebrating winter holidays in general. http://www.freedrama.net/songs.htm
"The Star" children's play and monologue