Why do batteries die faster in the cold?
Because a battery produces electricity through chemical reactions, and chemical reactions slow down when cold.
Inside a battery, ions must physically move through an electrolyte between the electrodes. Cold does two things to that process: it slows the reactions themselves, and it makes the electrolyte more viscous so ions move through it more sluggishly. The result is higher internal resistance, which means less current available and a lower usable voltage.
The important nuance is that the energy is usually still there. A cold lithium-ion battery has not lost its charge; it cannot deliver it quickly. This is why a phone that shuts down at 30% in the cold often recovers much of that reading once it warms up — the charge was never gone.
Car batteries show the same effect more dramatically, and at the worst possible moment. Cold thickens engine oil, so the starter motor needs more current at exactly the point when the battery can supply less. This is why batteries so often fail on the first hard frost rather than gradually.
Heat is a different problem. High temperatures let a battery deliver current freely but accelerate the side reactions that degrade it permanently. So cold causes temporary underperformance; heat causes permanent capacity loss. Leaving a phone in a hot car is worse for long-term battery life than using it in the cold.
Practical steps: keep devices in an inside pocket rather than an outer one, let a cold battery warm before charging — charging lithium-ion below freezing can cause lasting damage — and store devices you are not using at partial charge in a cool but not freezing place.
Battery capacity ratings are quoted at room temperature.