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We could not. Although, as seen in many experiments, we can spend a lot of time, months, without eating (only drinking water), provided that we have enough bodyfat for energy demands. Should one do it? I'd say no, unless under strict medical supervision.

This is highly unlikely, because there are no primates that hibernate. And our species originated in warm climates. When our ancestors migrated to colder regions, they underwent some genetic changes, the most notable one being pale skin to allow for more UV absorption abd adequate vitamin D synthesis, and very likely by the time they (and the Neanderthals as well) reached the Northern latitudes, they already were efficient tool users and skilled hunters and they made clothes. They would have had no reason to undergo a massive evolutionary change in so many systems, to evolve the capability to hibernate from scratch. Let alone lose it afterwards.

I would say this depends of your definition of “hibernate.” Early man likely spent 20–23.5 hours a day in his home, cave, or den during the coldest parts of the winter. Imagine how cold it was not having layers of clothing especially designed for warmth. Think how cold your feet would get without thick layers of soft socks and commercial footwear. You don’t even have to go back to prehistoric man, even in the 1800’s, many families would bundle up and sleep 14–16 hours a day, or at least severely limit their activity, because it was dark and in many parts of the world, uncomfortably cold.