Most batteries don't work as well in cold temperatures, but you might notice it most in your smartphone. It's common for phones (or tablets, laptops or other devices) to slow down or shut off entirely if exposed to extremely chilly weather.
Apple recommends using your phone only when temperatures are between 32 and 95 degrees (F) and storing devices at temperatures between -4 and 113 (F). If you do happen to leave your phone in the cold or simply use it outside and experience battery failure, it's likely temporary. Batteries should return to normal when brought back to an acceptable temperature. The same in not true, however, for extremely warm temps. Heat damage to batteries can be permanent.