Possibly the book is 1970s or early 1990s - but I'm pretty sure 80s.
It has a panda in it who dresses up as a polar bear. He has a white outfit (maybe made of a pillowcase?) and paints over the black bits or fur on his face with white paint (or flour?).
I think he's sad he can't fit in as a polar bear.
I also think the paint gets washed off in the rain, but not sure.
That's all I've got! Myself and DB vaguely remember it but can't remember any more!