Battery operated water heater?

Why do you want a water heater at your coop? If the coop is not to far from the house just run a hose off the faucet. I would not use hot water for the chicken even in the winter. You can buy heated waterers for the chicken just run an extension cord to the coop during the winter for that.
Except you house is over 100 feet from area coop is at and the driveway is in between. Gravel driveway not good for cords.
 
Battery powered water heater is a bad idea. Way too much energy needed.

I did calculate the voltage drop on a 200' run of 12 gauge copper romex wire, use the UV rated, gray color. At 16 amps of 110 volt, it drops around 12 volts. Fine for a resistant load like freeze wraps or an old school 40 watt incandescent bulb in a cookie tin with the water sitting on top of it. That 16 amps is way more than you would need, more like five or six amps which would be only 4 or 5 volts drop, safe for almost anything electrical if not optimal. If the distance was only 100 feet figure 6 volts to 3 volts drop, very safe for almost any sort of resistance heater.

You can bury the grey romex. Just mark it or carefully measure and record the path so you can not damage it if you dig any holes.
 

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