Usually, no. Most camera batteries are lithium-ion, and cold weather mainly causes a temporary drop in available capacity because internal resistance rises. In practice, the battery appears to run down sooner in the cold, but that does not normally mean permanent damage.

Once the battery is warmed back to room temperature and recharged, performance should generally return to normal.

The bigger risk is charging while the battery is too cold. Lithium-ion batteries should not be charged below 0°C, and it’s safer to charge them only once they’ve warmed to about 5°C or higher. Charging when too cold can cause permanent damage.

Using the battery in cold conditions is generally much less harmful than exposing it to high temperatures, which can shorten battery life more seriously.

So: cold use usually causes temporary capacity loss, not lasting harm, as long as you avoid charging the battery when it’s below its safe temperature range and follow the manufacturer’s limits.