Birds, fish, reptiles, amphibians, insects? Sure. But no mammals.
So I had to google it. Apparently, there is a sloth that moves around so slowly moss grows all over it and it doesn’t care. So it may appear green, but only in the sense that it wears it.
This is just a guess, but could it be that brown is more useful since mammals (at least the first ones) dwell on and in the ground, where brown would be more beneficial for survival?