The heat capacity of air is about 0.02 kJ/(mol.K)
That translates to 0.000693116635 kilocalories/(mol.K).
Or about 0.0000309 kilocalories/(Liter °K)
So heating a liter of air from -60°F (-51°C) to 37°C takes about 0.0027 Kcal.
The volume of a normal breath (tidal volume) is 6-7 ml/kg.
So a 100 Kg person will take in about 700 ml/breath.
If the outside air is at -60°F, it’ll take about 0.0019 Kcal to heat 700 ml of it to body temperature.
0.0019 Kcal is the amount of energy contained in less than 1/1000th of a single Pringles brand potato crisp.
Adding water vapor to the air will naturally increase the number of calories needed to heat it to body temperature.
I work at a store that has a couple walk-in freezers set to -20F, there are circulating fans inside that blow constantly, and it still takes about two hours before a 2-liter bottle of soda at room temperature begins to freeze up. If you leave the bottle in there just for a half-hour you can barely feel any difference; it takes about an hour before it even feels cool. So I’d guess, “no”.
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When I’ve been outdoor in 60 below temperatures the air is absolutely dry. Not a speck of moisture. I’ve done the trick where you toss a glass of water into the air and it comes down as ice crystals or sublimates before it hits the ground. At that cold the moisture holding capacity of the air is near zero.
One really big consideration is the wind. Where I grew up in Fairbanks Alaska there was typically no wind at all when it got really cold. I imagine if there was any steady wind the extreme low temperatures couldn’t last long as eventually warmer air would blow in. Add in the ice fog, the dead air, and the strange accoustic properties of the air and it’s like you are on another planet.
The main pain you feel at 60 below is your lungs, mouth and nose. The air is extremely painful to breathe in directly without a facemask. You lose heat pretty rapidly this way. I think this is the major route for heat loss at this temperature. Being naked would hasten your death, but not by that quickly. You might freeze your ears, toes, nose, fingers, and genitals within one minute, but I don’t think you could drop your core temperature beyond recovery in only one minute. If you don’t have shoes and your feet are touching 60 below rock or dirt you will probably lose your feet in a minute. If you can stand on snow you might do a little better since snow doesn’t conduct that much heat. But having to touch the ground with your bare feet is really bad news.
Jack London wrote a short story called To Build A Fire that describes in graphic detail what might happen to a person at extremely cold temperatures. In his story, a fellow is travelling the Yukon trail when the temperature was 75 below. Early in the tale, when the guy spit, it froze with a sharp crack before it hit the ground. The guy thought it odd and reasoned that it was colder than 50 below because at that temperature the spit cracked when it hit the ground. There are also several passages that deal with how quickly he lost feeling in his fingers when he removed his gloves. In the end, the guy dies because he has to take his gloves off to strike his matches when trying to build a fire, and his fingers go numb before he can accomplish the task.
Granted, this was a fictional tale, but given Jack London’s experiences during the late 1800’s/early 1900’s, I’ve always considered his scenario to at least be plausible. And, while it differs from the OP in that the guy was not naked and it did take more than a minute for him to actually die, his extremities were numbed and rendered useless in a very short time.
Can you die at all in one minute? If the brain is starved of oxygen how long does it take to die? Obviously serious head injuries kill the brain directly, but surely if you have just been frozen for a minute your brain would still be recoverable.