There isn't much forage in the winter here in Kansas, so I wouldn't guess there would be much in Ohio either. Bugs are virtually non-existent in winter, and even when there is no snow on the ground, there isn't much foliage either. Grasses and other plants stop growing in the winter and what is there goes dry and brown, losing most of its protein. If they eat it, they don't get much nutrition from it, and since it doesn't grow back, once its gone, its gone.
As for what you can supplement....there was a thread on here a winter or two ago about sprouting grains, that was an interesting read. I usually buy a bag of deer corn and give them some of that most days in the winter, as a treat. You can also try growing mealworms for them, although they progress pretty slowly in the cooler months too.