Here in MN, the power going out in winter is a real problem every winter.
I have a battery backup for the computer, but it only gives a couple minutes of life - long enough for me to shut it down.
My solution to how to keep eggs warm would be a bit different than an expensive battery backup.
I have camping gear, including a propane stove and several 1lb bottles of propane. I also have a ton of 1q screw-on-lid disposable tupperware rated for hot or cold foods. If the power went out, I'd boil some water, put it in the tupperware, and put those in the 'bator.
I have a full 'bator right now, and we're entering the nasty part of the year, so I have all that stuff on standby. I also have blankets nearby to quickly pull over the 'bators to keep the heat in.
That Guy and I recently bought metal canister thermos things that get really warm when hot water is poured in them. He goes winter camping and has field tested them - put in a sock, under the covers, they stay warm all night with enough warm water left in the morning to make cocoa/tea with. Those would get way too hot for the 'bator but they'll do just fine for /me/.
I also have several battery lanterns around the house, a propane tent heater, and a winter preparedness kit in the car that would put most survivalists to shame. I am a total freeze baby. I don't go winter camping and like heck would I be willing to "winter camp" in my own home.
-Spooky