Ducks have very little muscle in their feet, mainly tendons. This means that the muscle which makes them move is further from the feet and better insulated, and there's less in the feet to keep warm.

Ducks also have a clever circulatory system, where warm blood going down to the feet in arteries goes closely past the cold blood coming back from the feet in the veins.

This is called a counter-current heat exchanger, as heat is exchanged between the hot blood and the cooler returning, meaning that the birds do not lose too much heat through their feet, because the blood that reaches the feet has already surrendered most of its heat to the returning blood.

There is some suggestion that they also make an anti-freeze compound in their feet called ethylene glycol, which stops the blood in their feet from freezing by lowering it's freezing temperature. Natural anti-freeze chemicals are also often seen in fish that live in freezing waters.