Recently I have been discussing polar bears and their whiteness*. Some people seem to think that their whiteness helps them in catching prey and that is why whiteness won out over some other color, like brown. The point being is that they say polar bears evolved from brown bears.
However if humans were the prey that may make sense, but humans could spot a polar bear unless it was very dark out or there was a blizzard. So the whiteness wouldn't help. Other prey animals are smaller than the bears and that means their perspective is changed, they are looking up with the blue sky as the back-drop. Being white wouldn't help in sneaking up on those prey. Camouflage only works when it is used correctly, meaning it is all about the perspective of that you are trying to hide from.
Being white would protect the bears from attacks from above, though. But just what type of organism could attack and kill a polar bear from above, I don't know. Perhaps eagles could feed on polar bear young, so in that case white could protect them until they grew up.
There is one scenario that would help- polar bears in the water could resemble floating ice and that would allow the bears to sneak up on seals resting on top of floating ice.
OK winter is coming and it looks like that will be a good time to build a snow bear to check it out from different angles to see how it blends in with its surroundings.
* polar bears do not have white fur- it is transparent with a hollow core. the whiteness is an effect of light scatter and reflection. however there are bears that have white fur tat are not albino.