It happens every winter. You are outside in the cold, you take out your phone to check the map, and it dies. A minute ago it showed forty percent. Was the battery lying? In a way, yes.
Inside your phone is a lithium battery, and a battery is not a tank of electricity. It is a small chemical factory. Power is made by particles moving between two sides of the battery, and like most chemistry, that movement slows down when it gets cold. In freezing air, the particles move so slowly that the battery cannot push out enough power, and its voltage drops. The phone sees the low voltage, decides the battery must be empty, and switches off to protect itself.
The proof comes later. You step into a warm room, the chemistry wakes up, and the same phone turns on with thirty percent battery, as if nothing happened. The energy was there all along, just frozen behind a slow reaction. So in winter, keep your phone in an inside pocket, close to your body heat. The battery is not weak. It is simply not a fan of your weather.