Warm-blooded animals are able to do this because they have a high metabolism. This means that their bodies produce heat at a high rate, which allows them to maintain their body temperature. Warm-blooded animals also have a thick layer of insulation, such as fur or feathers, which helps them to keep the heat in.
Eagles have a very high metabolism and a thick layer of feathers, which means that they are very well insulated against the cold. This is why they are able to survive in cold climates, even when the air temperature drops below freezing.