Whats it going to hurt leaving the black or gray tanks dry? Think about it, if the tank is cleaned its just a plastic tank setting around and it doesn't care if its wet or not. Whats leaving 2 or 10 gallons in a 50 gal gray tank going to do, sure if conditions are right the little bit of moisture might evaporate keeping the inside of the tank a little wet but without the right conditions there is a hole lot of plastic not touching the water.
As for leaving liquids in the tank if its not full say 1/2 full there is plenty of room for freezing water to expand so there won't be any problem. The problem can come from freezing around the gate valve as most tanks let water into the exit pipe, freezing here can damage the gate valve and even the sewer pipe when it expands. If you must keep some water in the tanks then add the appropriate amount of anti freeze. I say save your money and leave the tanks dry.