Domesticated ducks are still outdoor animals. There is so much about happiness that revolves around foraging and playing in the mud and water that I cannot imagine they'd be happier indoors than out. Sometimes it is hard to imagine that they wouldn't prefer living life the way we humans do, but they are animals and have their own needs, desires and habits. I agree with those who say as long as they aren't downy little ducklings, give them constant access to an outdoor shelter from predators and the weather and observe them enjoy the cold and wet. Then ask yourself if you really want to deny them all of that to make yourself feel a bit better.
(I presume you're not living in an igloo!)
(I presume you're not living in an igloo!)