Eurasian eagle-owl
Even those near the northern limits of their range, where winters are harsh and likely to bear little in food, the eagle-owl does not leave its native range. There are cases from Russia of Eurasian eagle-owls moving south for the winter, as the icebound, infamously harsh climate there is too severe even for these hardy birds and their prey. Similarly, Eurasian eagle-owls living in the Tibetan highlands and Himalayas may in some cases vacate their normal territories when winter hits and move south. Even in those two examples, there is no evidence of consistent, annual migration by Eurasian eagle-owls and the birds may eke out a living on their normal territories even in the sparsest times.
Snowy owl
Snowy owls nest in the Arctic tundra of the northernmost stretches of Alaska, Northern Canada, and Eurasia. They winter south through Canada and northern Eurasia, with irruptions occurring further south in some years. Snowy owls are attracted to open areas like coastal dunes and prairies that appear somewhat similar to tundra. During irruption years when they are found in the Northeastern US, juveniles frequent developed areas, as well as the expected grassland/agricultural areas that older birds primarily utilize. All ages spend a fair amount of their time over water in the Great Lakes and Atlantic Ocean, mostly on ice floes. They have been reported as far south as the American Gulf Coast states, Hawaii, southernmost Russia, and northern China.
In the Late Pleistocene the range expanded southward to Bulgaria (80,000–16,000 years, Kozarnika Cave, W Bulgaria), and much of the Italian Peninsula.