By far the cheapest and easiest solution....so it makes the most sense.Folks kept chickens for centuries before Thomas Edison and yes, even in bitter cold climates.
Folks carried water for their birds, morning and afternoon, every day, day after day. Keeping the birds properly hydrated is essential, of course. The rubber bowls make removing the inevitable ice formations easy to remove.
Apart from running electricity, I know of no other alternative than watering in the early morning and again in the afternoon. BTW, carrying the water in a couple of old milk gallon jugs give you a handle and there's less chance of spilling, on the way out to the coop.