My runner ducks are easier to care for in the winter than my chickens are. Ducks seem to enjoy the cold and snow much more than I do!
Mine live in what is really just a wood-framed, 3-foot-by-10-foot box, wrapped in hardware cloth for the walls. It has a roof with a door that opens on the top on one end and a door for them that opens on the other end. In the winter, I put a tarp over the top and add plywood walls to both ends to keep snow from collecting inside the shelter and offer more of a windbreak.
It gets cold here -- sometimes days below zero in a row -- and they seem unconcerned. In fact, when the chickens are snugly cuddled up in the coops, the ducks are often lying out in the snow. Ducks are built to be waterproof, and as long as there is open water, they will want to climb in.
I don't leave their kiddie pools out in the winter -- I once read about a goose that got its feathers frozen to the ground after going for a swim!
But I make sure the runners have a water bowl deep enough to dunk their heads and keep their nares clean. Of course, since they are ducks, that means I sometimes see someone trying to bathe in the too-small water dishes. No incidents of frozen feathers, though!
Hope this sets your mind at ease, at least a bit!