The significance might be related to the Christmas spirit in a cold, wintery setting. Maybe Randy's dressing up shows his excitement for Christmas. It could also be a way to stay warm during the cold winter days while participating in Christmas activities.
Since there's not much information, Randy could be just a fictional character in a Christmas - related story someone made up on the spot. It might be a name given to a character who was being annoying during the story, so they were told to shut up.
I'm not entirely sure without more context. 'Shut up' is a rather rude way to tell someone to be quiet. 'Randy' could be a name. And 'Christmas story' might refer to a story related to Christmas. It could be a line from a movie or a personal interaction where someone is telling Randy to be quiet during a Christmas story.