Antarctica is generally colder than the Arctic. They would almost certainly be stuck along the coastlines of Antarctica like the penguins are, since the interior average temperatures rival the coldest ones ever recorded in the Arctic. They should be fine there, but then that means they have a very limited distribution and that penguins and seals consequently are always forced to share an environment with the polar bears. Because they’re not used to the polar bears, their populations would likely be destroyed, leaving the polar bears to starve. Unlike in the Arctic, too, they would have nowhere to retreat if their food supply ran out. Outward is hundreds of kilometers of ocean, and inward is hundreds of kilometers of unsurvivable desert.