Polar bears appear white for the same reason that a pile of snow looks white—reflection. If there are a lot of surfaces that reflect light (either in the polar bear’s fur or a snowdrift), then any light that hits the object will be bounced around many times before coming back toward your eye. Most wavelengths of light are scattered equally well, so you end up with the object looking white (in other words, no wavelengths are absorbed, which would give rise to a color).