I go out every morning to let the kids out and when it gets cold enough to freeze I kick the pan to break the ice and pour hot water on top and it keep it liquid most all of the day. At night they are in the sleeper and do not need the water. We have heat out there and I have heard others say heated dog bowls and such but you are like others with no electricity or do not want to spend money. The other thing I do is bring in the bucket at night and put it on the back porch so it does not freeze at night and put it out in the morning when I go let them out of the coop.
Extension cords are great. I have one outlet about 50 feet from my coup and I have a long extension cord. We have a heater under the water which is very very useful! When I first put it out there, I thought the chickens would peck at it but they don't.
I also have no electricity. I tried what someone else tried, take some rocks heat them up in boiling water for say 10 minutes, pour out the boiling water and add the rocks to a rubber tub with water. I tried it and it worked for for me. I bring my waater in at night and at 5 Am I go give them their morning water.