Matella,
Our Buckeyes are on pasture during the day and cooped at night. During the day they forage both in and out of the coop (which definitely saves $$$ on feed). I've seen our girls eat snakes, lizards, bugs (of course), scorpions, moles, and even chipmunks (no lie!) but their favorite warm blooded treat is a field mouse. Should any hen actually catch one since they're quick and usually never far from the bolt holes they dig near food sources like feeders, that hen will take off running to be sure she's the only one who gets the morsel. Very comical.
At night I take up the feeders to keep the little nuisances from getting too much of a free meal ticket. I hate trying to pick tiny mouse pills out of the feed. There's enough spilled feed on the coop floor (dirt with a deep litter system of mulched oak leaves) that I know I'll never really be rid of the lil' varmints, but the girls really do keep us from being over-run. We rarely use artificial light on our girls so as to let them cycle through rests in laying naturally, but I have heard stories from folks in northern latitudes that use artificial light on timers and their girls have accustomed themselves that when the lights go on so does the hunt- on goes the light, mice freeze in surprise, girls swoop down from the roost for a treat!
I will add this last observation. Foraging is an instinct. All Buckeyes are hatched with it. But, like many other things, foraging is a skill. Some birds will be better than others at learning to forage for themselves. Fortunately, other birds are able to learn these honed skills by the example of other good foragers. If you want your girls to get as independent in foraging as possible, raise them under a hen. Experience has instructed us that hen raised chicks are more active and independent foragers AND these skills are magnified in each successive generation! Hen teaches chick her skills. Chick adds new experience to these skills and passes them on to the flock and to future chicks. Example: our pasture raised chicks learned two years ago to follow the cattle for bugs they scare up, to scratch out the dung pats and to hunt the horse flies that plague the cattle. These were skills that were not present in the flock in previous generations but were added and preserved through experience passed hen to chick.
Horses ran out, but chickens were fast asleep at 3 am and had no chance. 
Below is my little fuzzy ball of Buckeye right in the middle of all the teens .... scrappy little girl. 
