Batteries in the cold

Your phone did not run out of charge. It ran out of the ability to deliver it.

A lithium ion cell works by moving ions through an electrolyte. Cold makes that electrolyte more viscous and slows the chemistry, so internal resistance rises. The energy is still stored. The cell simply cannot deliver it fast enough.

Why it shuts down early

When a device draws current, higher internal resistance causes the voltage to sag. The device reads that sag as an empty battery and shuts down protectively, often at an indicated thirty or forty percent. Put the same device inside your jacket for twenty minutes and it returns with much of that charge apparently restored, because it was never actually gone.

Do not charge below freezing

This is the one that causes permanent damage. Charging a lithium ion cell below roughly 0 C encourages metallic lithium to deposit on the anode instead of intercalating into it. That deposition is largely irreversible, it permanently reduces capacity, and in the worst case it grows structures that can short the cell internally. Warm the device first, then charge. Many modern devices refuse to charge when cold, which is a feature and not a fault.

Practical measures

Carry phone and power bank in an inner layer against the body, not in a lid pocket.
Warm a cold device before charging, not while.
Overnight, the battery goes in the sleeping bag.
For anything taking AA or AAA cells, lithium primary cells hold up far better in cold than alkaline, which fall off badly below freezing. They cost more and last enormously longer in winter, and they are lighter.
Flight mode saves real power and does not disable satellite positioning, which is receive-only and works with no network.

Storage

Long-term, lithium cells last best stored around half charge and cool. Leaving a power bank fully charged in a warm cupboard all winter costs you capacity you will notice next season.

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