Fawns (baby deer) have white spots on their backs. Take a look at the picture below from this past month.
The answer to this question is that fawns have spots because it helps them camouflage better in the woods.
Fawns spend a lot of time laying down in grass and leaves that are under canopies of trees. Sunlight comes through these trees in beams that make bright splotches on the forest floor. The brown color of the deer's fur and the white splotches look similar to brown leaves and dirt mixing in with the sunlight that hits the forest bottom.