Here is the first-hand account of a family who lived without power for 13 days after Hurricane Ike, in 2008.
A short excerpt:
"My first bit of advice for your kids is that you focus on what needs to be done and NOT leave the news on all day so they can hear that doom, gloom and devastation are on their way. My younger daughter who has been potty trained for months had 2 accidents on Friday before the storm. She was very clingy and whiny. It serves no purpose for them to be scared more than necessary. My suggestion would be to have a TV or radio on somewhere away from the children so that you can have up to date info without having them have to worry.
During the storm my older daughter slept the whole time so we didn’t have to comfort her or keep her busy at all. The 3 yr old was agitated and awake a lot of the time. We kept her occupied by letting her hang with Dad and make sure everything was ok, she had her own flashlight and stayed right with him. Giving her a job seemed to really keep her mind off of things, and hanging out with Dad helped her to feel safe."
It is great to learn from someone who has lived through something like that!