I do my best to work around the weather. A fridge that is properly loaded in preparation for a storm, and kept closed as much as possible, should be fine for up to 24 hours, a freezer, up to 48 hours.
That said, look at the weather and chose you time to operate that genny. What I find, is too many people wait too long to fire it up, then the poor fridge, freezer, and house heat have to play the catch up game. I'll wait a hour or two after the power goes out, and if the weather isn't terrible yet, fire things up then to maintain them rather than waiting 12+ hours. That way, even with a 1/2 hour or 45 min break in the weather, I can keep things in good shape. If the fridge/freezer has warmed up already, a short burst of run time won't hardly do squat.
In the end, as Dex said, do what it takes when it takes it as smartly as possible. Just don't put something near that genny that the exhaust could catch fire.
The genny pictured below is one that I fixed last night to help a buddy out. It belonged to his step-father who was a contractor. I worked with the man in the past, and can say that the looks of this generator doesn't tell 1/2 the story of what it has been through in it's 5 years in service. The owner died one year ago, and the buddy was hoping to get this genny going to help out with the siblings. Even after being operated through rain, mud, snow, etc, etc, the only real problem this unit had was that the magneto cover, housing the pull start, came loose some time ago and was allowed to operate that way. As such, it basically vibrated the small actuating tabs on the plastic dogs for the pull start down to little to nothing. That abuse, accompanied with the wet conditions / dirt / dust / mud just kept them from flying out and turning the engine over. After some cleaning, and playing tinknocker, riveting new steal on to secure the housing, the genny is good to go for this storm, but should have a new cover / pull cord mechanism purchased for it.
I doubt, considering you are concerned enough to ask, that your genny will ever be in the conditions that this one has seen (or the use).
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