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I had a phone go completely off on multiple occasions doing winter runs in tahoe and it wasn't even that cold (like mid-20s but with wind) so it's not so simple. And yes nearly 8000m peak it's common to have -40° temps

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> Many lithium battery formulations work in colder

It's possible, in fact probable that your phone doesn't have one of the aforementioned formulations.

These guys aren't using their cell phones to keep warm, I'm quite sure. It's true that Lithium Ion Polymer batteries, so very popular in portable rechargeable devices (and prone to the occasional thermal runaway) usually don't do well below 0°C. But that's not likely to be what they'd choose for such a mission. Simple Energizer brand AA/AAA disposable lithium batteries work fine down to about -40°, and can generally power heated socks and gloves etc. without any modification, and aren't particularly expensive given their considerably greater energy capacity and much wider temperature tolerance over alkaline formulations. The disposable lithiums weigh a good bit less than alkalines, too...for, you know, when every gram counts?

Edit: Also, these batteries aren't necessarily exposed to outside temperatures. Strategically placed near the body, they can be kept at higher temperatures for greater power efficiency - but if they are exposed to outside temps, they will not die as easily as your (pathetically useless in this situation) cell phone batteries would.

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