They stay during winter because ducks' bodies have a nice layer of cold-resistant fat and multiple layers of feathers for keeping the water out and the heat in.
They can also tuck their feet up against their bodies and, unlike chickens, don't have cold-vulnerable combs on the tops of their heads.
Ducks can easily handle up to -20°C and like to waddle around in the winter ponds, dive in the water or just chill on the ice or snow.
Here's some pictures of just that taken in Scandinavia in mars this year.
