As bald as a coot
Coots are water birds whose heads have the appearance of baldness. This doesn't refer to the lack of feathers on the bird's head, but to their white markings. 'Bald' has several meanings, one of which is 'streaked or marked with white'. That's the meaning here, as in 'piebald', used to describe the black and white markings of a horse or other animal.
The phrase is very old and is referred to in John Lydgate's Chronicle of Troy, 1430:
"And yet he was as balde as is a coote."
See other 'as x as y similes'.