I reckon they'd head straight for the North Pole when the Antarctic Winter was imminent, and do the reverse when the North Pole began to cool for winter. By that time they'd need to do so. They'd have burned off all their fat in the flying.
Poor things! They'd be a skinny as vultures after just one season. Why they might not even make it back from the Northern Ice sheets. And Antarctica would be completely without them.
I guess that's why 'The Good Lord' ensured they could not fly, eh?