Humans need socks, boots and all kinds of things to keep our feet warm. What do birds do to keep their feet from getting cold?
Q. I wonder . . . why don't birds get cold feet?
A. Actually, songbirds do get very cold feet: the surface temperature of their toes may be barely above freezing even as the bird maintains its core body temperature above 100°F (38°C). But most birds don’t succumb to frostbite because there is so little fluid in the cells of their feet, and because their circulation is so fast that blood doesn’t remain in the feet long enough to freeze.
We don’t know if cold feet bother birds like Common Eiders or Snow Buntings. We do know that they have few pain receptors in their feet, and the circulation in their legs and feet is a double shunt— the blood vessels going to and from the feet are very close together, so blood flowing back to the body is warmed by blood flowing to the feet. The newly cooled blood in the feet lowers heat loss from the feet, and the warmed blood flowing back into the body prevents the bird from becoming chilled.
(Answer from Cornell Lab of Ornithology FAQ page).