If you decide to run power to the coop, you should consider using SO/ SOE cable. It's rated to be buried in the ground. Romex isn't. The SO cable is pricey (compared to Romex) but would offer piece of mind. A floating de-icer would work for water.
We have had 8-12 chickens for a few years. We always get cold hardy breeds. We have an enclosed coop. No heat, no lights, no electricity - chickens do just fine. Lay eggs all year long.