Birds have a sort of thin extra eyelid called a nictitating membrane that protects their eyes and may do so in the rain.
The membrane is not entirely transparent, so the birds may not see clearly, but they can probably see light and dark.
As in cats, dogs and other animals, this membrane can flick over the eye very quickly to protect it.
It guards against collisions when birds are crashing through brush, and in birds of prey like the peregrine falcon, it closes immediately before impact with victims, covering the eyes as the bird grabs its prey.
