Fur has a thick layer of protection to help protect..say a bear in this case. A polar bear's fur is helpful in the cold, to prevent the bear from freezing to death.
But since a polar bear eats fish and things that it's used to in Antarctica, it probably won't adapt as easily.
Polar bears have fur to stay warm since the temperature where they live can get down anywhere from 0 to -30
However should that polar bear move to the forest he would have to learn to adapt to the new temperatures and humidity (lose most of its fur most likely)