Echoing what all the others have said, the choices I found were to contain the chickens or accept the poop. I took over year-old hens in March. There was snow. With the sun's low angle, there was a small, ~4' wide strip of yard that would melt. The chickens avoid the snow. They spent their time scratching and pooping in that strip, which also started to get muddy. I was losing my mind over the poop and the mud.
After a month or so, I built a yard exclusively for the chickens. Their yard is sectioned off with 4' chain-link fence. I also removed the grass from their yard and replaced it with sand under the coop and run and a
meadow seed mix for the rest of the area. To allow the seed to take root, I had to continue to allow the chickens to free roam the whole yard for more than a month. In the meantime, the yard dried out and the chickens starting accessing the entire yard rather than just the 4' strip. I learned that chicken poop dries out pretty quickly, and the dried poop doesn't get on your shoes. Most fresh poop--not cecal poop--from my grass-eating chickens comes off my shoes quite easily. If they poop on the patio, it dries out and is easy to clear off before anyone wants to use the patio. So, my four hens in the back yard of a 0.15 acre total suburban lot were manageable over the summer. Winter has yet to truly arrive here, with only one dusting of snow so far. I therefore can't say whether I might start losing my mind again with free-roaming chickens who are traversing narrow pathways to avoid snow.
In early November, though, a hawk showed up looking for an easy target. I've since hung bird netting over the chickens' yard to keep them safe from the hawk, and I no longer allow them free run of the entire yard. They are definitely less active than they were before. Now they spend most of their time in the dust baths, whereas previously they spent most of the day walking the entire yard, pecking the grass and bugs, and scratching at the ground (without causing damage!).
The chickens' yard is approximately 14' x 35'. Honestly, I feel a bit guilty about confining them there, even though it's to keep them safe from the hawk. Like I said, their behavior has changed since being confined because they don't have the same opportunities to express all their previous behaviors. And being back to the low angle of the winter sun, that space gets just a sliver of sun for a short time each day. I'm considering doubling their yard continuing the bird netting over the expanded area and likely giving them supervised access to the entire yard like KyCoop. DickMidnight's 50' x 50' enclosure is a better compromise than my space, even once I double it, and it sounds like you have the space to similarly provide them a larger zone.