I would strongly recommend NOT leaving any food of any sort out overnight. rodents are very slick about getting through just about any confinement to find food. and they're fairly habitual, they'll keep coming back until there's nothing for them to eat.
The way my coop is set up, the girls can go in and out of the coop for food and water whenever they want when they're inside the run. I have two flocks, one free ranges all day, and one that stays in the coop/run(they're younger). So since I have to keep the run door closed all the time, I leave a waterer outside for the big girls, and their food during the day is bugs and grass. soon I will be able to leave the run door propped open all day and they'll all come and go as they please during daylight hours.