Consider that animals adapt to suit their environment. A snow shoe hare lives in a tundra biome full of snow. Snow is white. Therefore it's good to have white fur so you're not easily seen by predators.
As for bats, having black colored fur is good because they are active at night when it's dark. When they're hunting for flies and such, they probably don't want to be seen. They also don't want to be seen by predators also so black is good camoflauge in this situation.
rabbits have a variety of colors that vary on the location of the breed as well as the season. both bats and rabbits are colored the way they are to camouflage themselves. bats are nocturnal and live in dark places, so they have dark fur to blend in. rabbits may have to blend in to grassy areas, forests, and snow, so they have a variety of colors
There are several other reasons for hair color than the amount of sunlight exposure.
hair gets lighter when its exposed to sun i thought, skin gets darker
