What do you you do in the winter for your pet bearded dragon if the power goes out?

It depends how long the power is off for. If its just an hour or so, it will be fine - as the heat will stay reasonably high in the vivarium. Longer than that - consider using 'heat packs' - they're small squares of sealed chemicals, that give off heat when activated (think glo-stick). Companies use them when transporting reptiles over long distances to maintain some heat. Heat packs can be bought at any time and stored until needed