A polar bear's outer coat is made of guard hairs that contain no white pigment at all. The hairs are transparent, with a rough, irregular internal structure that scatters incoming light across all visible wavelengths. Scattered light of every wavelength reads as white to the eye, which is why fresh snow, sea foam and unpigmented hair all look the same colour.
Under the fur, the skin is black. The coat has two layers: a dense underfur for insulation and longer guard hairs that shed water. The guard hairs are hollow along part of their length, which adds buoyancy and helps trap air, though the old claim that they act as fibre-optic light pipes carrying warmth to the skin has been tested and rejected.
The scattering is imperfect in practice. Bears in warm zoo enclosures have turned visibly green when algae colonised the hollow cores of their guard hairs, and wild bears often look yellow as the coat ages and picks up oils. What remains genuinely uncertain is how much of the coat's insulating performance comes from the hollow cores versus simple trapped air between hairs.