You are in a colder snowier climate than I was raised in, but I'll tell you how my parents handled their chickens.
We never locked the hen house door. The chickens were not restricted by a fence in any way, except the fence that kept them out of the garden. The hen house was in a pasture field, not that far from a barn full of hay, and not that far from a woodland. We would go years without a predator attack, but then a fox or something would find the chickens and have to be dealt with. Most would sleep in the hen house but some roosted in trees outside, even when the weather got below zero Fahrenheit. I'm mentioning this to show mainly that they were not coddled pets but were considered livestock and probably meet your definition of "wild".
The only time we ever fed them was when there was snow on the ground. Other than that they foraged. There was a barn full of hay nearby and sometimes some would go inside there and eat some of the seeds on that hay. We fed hay to cattle outside on the ground and they could get some of the grain that the cattle missed, but there was not a mad rush by the chickens to that potential food source when we fed the cattle, so I don't think they depended on it too much. Even in the winter with all green stuff dead, they could find vegetative matter and grass and weed seeds to eat. If there was snow on the ground, we would shell corn and feed that to them, but not unless there was snow on the ground. Some of the first year pullets would lay through the winter, but the older hens would molt and stop laying. The eggs were not double extra huge sized like you can get if you stuff the hens with extra protein, but they were decent sized when they did lay. During the summer, they laid very well and the eggs were decent sized.
These were mainly chickens raised by broodies, not raised in a brooder. I've noticed with mine that broody raised chickens forage much better than brooder raised chickens. Practically all the chickens made it through the winters and summers. These chickens were a barnyard mix, mainly mutts, but with Rhode Island Red, Dominique, Australorp,some game, and who knows what else in their background. Occasionally, but not that often, Dad would pick up a dozen chicks from the Co-op and raise them in a cardboard box on the back porch to bring in new blood. At about 5 or 6 weeks old, he would turn them loose and they were on their own. Most of those made it, but they had the other chickens to learn from.
I don't have any scientific studies to refer to. Just my memories from a lot of decades ago. It is a different world now. Thanks for the chance to go down memory lane.