Also birds’ feet are mostly bone and tendons, so unlike mammals, they have a limited supply of nerves, blood vessels or muscles to freeze. Their feet are also covered with scales which isn’t a living tissue and less susceptible to freezing.
Finally, birds don’t have sweat glands in their skin to produce any moisture to freeze. Heat and moisture are accumulated in sacs, transferred to the lungs and eliminated through the mouth. No moisture escaping through their feet is also the reason they don’t stick to metal perches in the winter.