They won't starve, if that's what you are thinking. If they don't have a light, they should sleep all night anyway. But it shouldn't hurt them to go without overnight, though their bedding will still be wet. Have you seen their poo?
Clean, dry hay is not an option. Oh....hay....I would probably leave their feed in there, just so they don't eat the hay instead. You should probably think about using pelleted wood or wood shavings as bedding. The pellets work very well, you would be amazed!
