I suggest building on to your existing shed. If you are free-ranging in your yard, you don't need as much space in your coop as people who don't free-range. 4x4 is adequate for 4 hens who are only using the coop for nighttime roosting (more space is always better, though). In the winter, you could put up an open-ended covered hoop house as a kind of "porch" to the night coop, so that they could get out and move around some. You could leave that up year-round, or take it down in the summer after the spring rains. Also, most common chicken breeds don't need warmth; they need ventilation. Winters get into the negatives where I live. I have a lot of ventilation, and I only cover it up during really strong wind events (and then open it back up as soon as the strong wind passes). I don't heat my coop, and I never fully seal it up, even in the worst wind. (If you have breeds that are only suited to hot weather living, then obviously, this advice does not apply.)