When a device gets too cold it can cause the battery in the device to drain and lead to slower performance and even temporary or even permanent damage to any internal components in the device including even damage to the screen if it has one.
Cold temperatures can cause lithium ion batteries to lose their capacity and drain faster than they normally would.
Extreme cold temperatures can cause the device to not operate properly and the battery may not be able to hold a charge and lead to the device shutting down.
The charging of the battery may also be effected and slow it down or stop the charging altogether.
I once tried booting up a desktop computer that was in my cold house after the power had been out and the house was still freezing.
The computer finally booted up but would not respond correctly until the house got above freezing.
So in extreme cold temperatures it can be too cold for the computer to even work properly.
For other devices touch screen sensors can become less accurate in cold temperatures and the screen may even become rigid and even shatter or break or crack.
Cold temperatures can also cause any internal components in the device to become more brittle and fragile and the device may even register errors or have difficulty in performing certain functions.
Also when a cold device is brought into a warmer environment then condensation can form inside and potentially lead to damage.
Some devices are more tolerant to cold temperatures than others.