While watching the migrating geese resting on a lake with a coat and hat and gloves on and still feeling chilly, it's amazing to see the birds swimming atop the icy waters. Sometimes I imagine being a goose, duck, or swan migrating during the winter. Unlike some birds that seek shelter from the elements, they remain on the water. Although they have waterproof feathers atop down feathers to keep their bodies warm, their feet are still exposed to the icy waters yet they are not frozen.
The key lies in counter-current heat exchange. In the legs of ducks, geese, and other types of birds, the arteries (blood flowing away from the heart) have branches that are very close to branched veins (blood flowing towards the heart), allowing the warmer blood flowing towards the feet to cool, and warming up the blood coming up from the feet. This way, the foot is kept colder; without the branched blood vessels, the blood that reaches the foot is still warm.
At first it might not seem to answer the question, as it seems to be that they keep their feet warm by making their feet cold? Well, the point is not to keep their feet warm, but it is to make them colder so that the heat needed in other parts of the body is not lost. This works because body heat is lost when the outside environment is colder than the exposed tissue, so the less the different in temperature in a goose's exposed feet with the water, the less body heat will be lost. To reduce the amount of heat lost, they also reduce their surface contact with ice which (according to askanaturalist.com) is the reason why you might see them balancing on one foot at a time.
Heat exchange also prevents cold blood from cooling down the parts of the body covered by feathers as the blood flows back towards the heart in the veins.
This heat exchange is also applied when a bird is in a very hot environment, as it keeps it from overheating, as well as with other animals such as marine mammals, which have a net of branched veins and arteries around their bodies below their skin to protect them from the cold in addition to fat insulation.
AskANaturalist.com. Why Don't Ducks' Feet Freeze? Ask A Naturalist. Retrieved from http://askanaturalist.com/why-don%E2%80%99t-ducks%E2%80%99-feet-freeze/
Eccentricscheinstist.wordpress.com. Why Don't ducks get Frostbite? Wordpress. Retrieved from http://eccentricscientist.wordpress.com/2007/01/13/why-dont-ducks-get-frostbite/