We have heated water tanks for the cows. Fil used one hooked up to the lp tank, when they needed to be replaced, he bought electric ones.
When we had rabbits, I just took out a 5 gallon bucket of water from the house, set their frozen metal water bowl to float in the bucket. The ice would melt enough to pop completely out and we'd re-fill the bowl. Happy bunnies.

We did this 2x--morning and evening.
On a rotational note, we have three (sometimes more if needed) 5 gallon buckets that we fill in the basement. I fill the buckets at night, 1. so if the power goes out, I at least have water for them in the morning and 2. the water warms up a bit more. In the morning, I just switch out the buckets in the pens, bring them in to thaw out and then fill up for the evening chores.
I use those black rubber bowls for the fowl and just throw them on the ground to bust out the ice, but I have found if I empty them in the evening, it hasn't got a thick layer of ice on it so it's not as hard to dump out then rather than doing it in the morning.
I've done this for many years as I don't use electric in any of my critter houses, and it's worked rather well.
Would a basketball or one of those jolly balls they sell for horses work in the water tank, as opposed to a chunk of wood?
jd