Why doesn't my (battery-powered) light work in the cold?
Batteries, especially most types of rechargeables don't work well in cold conditions. The chemical reaction that powers the electric voltage does needs some temperature to perform as intended. If you then have a consumer load that requires a bigger amount of power, they tend to drain rather quickly since they cannot set free much energy when cold.

You could try with newer batteries, maybe yours are already a bit exhausted or you can try ones that are based on a different cell type.