We've been free-ranging our flock for 10+ years now in the forest surrounding our home and here are a few things we've observed about their "natural diet" tendencies and foraging:
Seeds from flowers and grasses/grains fall and are eaten off the ground (and right out of the waning plants) throughout the late summer and fall, sometimes even into winter. It is amusing to watch the little bantams jump up to grab seeds out of the dying stocks.
Berries from native serviceberry, chokecherry bushes are eaten when ripe in late summer but then also dry on the bushes and the chickens snag them into winter and again find them in the spring.
Bugs generally are only available during the warm season here, which is from April to October. The meager exceptions to this are flies and spiders that might "winter" in the crannies of the coop and come out during a warm winter spell...rare delicacies for the birds at that time. Worms and mosquitoes are summer delicacies, grasshoppers have their own season in the late summer and the birds run around hunting them in a frenzy! They scratch rotting logs open to find termite grubs. Mostly, when the ground is open and there's green grass, they graze on it. Don't have serious interest in many other greens than grass, altho they'll decimate my garlic patch when the shoots are young.
Our snow pack in the mountains is much too deep in the high Rockies (8200' elevation) for most birds of any sort to winter over here naturally. Except for predator birds, like eagles, owls and falcons, that live mainly on mice and other burrowing creatures and fish from the river during the winters. Our songbirds and wild turkeys go elsewhere, lower elevations where they can find open ground/seeds all winter, and then come back in May.
Chickens may not be able to live wild/naturally here year round, without human husbandry, but they are very capable of foraging quite well for themselves when the snow is gone. Although we do put out grain (and household leftovers and also yoghurt and garlic) in the warm months, they rarely touch the grain. Our feed bill for a large flock is almost non-existent until winter comes, as they prefer to find food for themselves.
And, yes, they do lay very well during the warm months. Ours have been quite robust and healthy, living long lives and laying into old age.
In an urban setting, one could work toward a natural, self-sufficient way of keeping chickens by planting bird-friendly bushes, sunflowers, a grain plot if there is room, and a garlic plot. And perhaps keep a mealworm bin in the basement!
