Electrochemical cell potentials are temperature dependent, as is the forward voltage drop of an LED. If the current through the LED is regulated with a simple series resistor, then the output of the light will be temperature dependent. If the LED's are held at constant current, then light output won't change. So the behavior of the light at low temperature is really a design issue, probably driven by how much you want to pay.

Likewise, simplistic charging circuits could suffer from similar issues. Lithium batteries are a special case because they have a thermal runaway mode, and can asplode if they're not charged under the correct range of conditions.