I have heard of people putting those plastic grocery bags over their socks.
+1, I'm one of those people. Foot in sock in grocery bag in shoe. Trim with scissors around the ankle if you care. That's for warmth.
For rain, it is foot in sock in shoe in bag, wrap the handles around your ankle and tie snugly. Rip one or both handles if additional length is needed. Don't worry about cleats/pedals, plastic shopping bags are thin and flexible enough to not interfere with clipping in. Bag may only last for one ride, but that's the point of being disposable.