Sorry, it'd take a pretty big battery (deep-cycle, i.e. expensive) and you'd be having to recharge it all the time or wire up some pretty significant solar panels to it.
Depending where you are in KY and what your coop is like, it is quite possible that you will not have to deal with the waterer freezing *that* much of the winter. I don't know whether your existing waterer is plastic or galvanized, but if it is one of the double-walled galvanized drinkers, DO NOT let it freeze period, as that can irreparably bust it.
The simplest thing, frankly, is just to put a bucket of water out there during the day (does not have to be huge i.e. you don't have to lug gallons and gallons of water around) and in the morning either remove the frozen skim from it or if it's too frozen for that then upend it to thaw/drain and replace with a fresh bucket of water. As long as you do this -- ensure that they start the morning with liquid water -- it is ok for it to freeze overnight, as chickens do not drink in their sleep <g>.
Beyond that, remember that a) larger volumes of water freeze more slowly than small containers, and b) you can make an insulated thingamabob to enclose the container or for it to sit on, or both.
Good luck, have fun,
Pat