If by some chance she did hatch out ducklings in winter she would take care of them. There is no babysitting.
We're talking about a runner - so I doubt she would brood them in the first place - but with my luck you never know. Plus where we are it is cold and windy in the winter and my barn door stays open 24/7 for my donkeys, so again - brooding ducklings in the winter - nah! Egg patrol will be in full swing.