Well, perhaps there's a story where a duck is chosen to be the centerpiece of a grand Christmas feast in a small town. But the children in the town feel sorry for the duck and they convince their parents to let it go. So, on Christmas day, instead of being on the table, the duck is set free in a beautiful meadow. And the town starts a new tradition of having a vegetarian Christmas dinner from that year on, all because of that one little duck.
One possible 'Christmas duck story' could be about a little duck that lives near a pond. On Christmas Eve, it sees all the lights and hears the carols from a nearby village. The duck is curious and decides to explore. It finds a kind family who leaves out some food for it. The duck then becomes a sort of Christmas mascot for the family that year, and they make a little shelter for it in their yard during the cold winter days. This simple act of kindness towards the duck makes their Christmas even more special.