If I am baking cake or cookies in the oven and I lose power, what should I do?
Does it make to sense to leave the cake/cookies in the oven until the power comes back on, or should I take them out?
When/why would I need to leave them in the oven vs. take them out?
Removing things from the oven halfway through is not very friendly to baked goods. In general, they'll collapse as they cool off since the structure isn't cooked and set, and the leavening (baking soda/powder in these cases) will be spent, so there's no way to get what you originally wanted. It might be something like what'd happen if you forgot the leavening in the first place.
In general: if there's only 5-15 minutes left, just leave it in, and the heat retained by the oven will take care of things. If it's barely started - just beginning to get warm, not bubbling/rising much - probably best to take it out and wait to bake later, especially if it's something that can survive waiting at room temperature. Anything else, leave it in and hope the power comes back; it's going to be ruined if you take it out and ruined if the power doesn't come back on so you might as well go for it.
So for example, cookies could probably survive this by leaving them in. They don't have very long baking times - somewhere in the 5-15 minute range. Your oven won't cool off all that much in that time without power. So if you leave them in for a little bit longer than the original baking time, they'll probably be fine. If your oven has a window, look in with a flashlight to check on them - you don't want to open it to check them.
A cake is iffier. If it's 15 minutes into a 45 minute baking time, you may just be out of luck. I think I'd still leave it in, hoping that the power comes back within 5-10 minutes, in which case it'd probably make it. As I mentioned earlier, if you lose power early and for long enough, the cake will have spent its leavening and collapsed. You could finish baking it, but it'll still be collapsed - it probably won't have a terribly palatable texture (definitely dense, maybe chewy).
The only time this has actually happened to me was with some cornbread muffins, around 2/3 of the way through their baking time, and the oven didn't have a window. I wildly guessed how much extra time to add, pulled them out then, and they were great. So there is hope!
My main considerations would be:
How long does the power regularly go out for? I live in an area where power outages are typically quite short, but once in a while they're hours or days long; as the power typically comes back on within 5-10 minutes, I'd leave everything in the oven.
How much time is remaining? If it's just a few minutes, leave it in, and check on it a few minutes after you think it would be take, as when you open the door, you're going to let the remaining heat out.
Do you have some alternate way to cook it if you take it out now? For example, if it's cake and you have a grill or firepit and the right tools, you might try one of the camping suggestions. But I'd leave it in the oven to continue baking while you prepared the alternate cooking source, so it's not coooling off (as much) before you transfer it.
Follow your nose to determine how long to finish baking an item where the power failed. Baking is often finished by the familiar aroma caused by the "Dry Heat" that happens as the moisture evaporates leaving behind carbohydrates that begin to caramelize, or experience polymer thermal break down. Some times the fillings and crust do not always finish at the same time though; which leaves a delicious mess to enjoy at home rather than at a social event.
