Do electronic devices consume more power when the ambient temperature is cold?
It's the opposite, actually.

Your devices are made up of individual electrical components, while datasheet for the devices are harder to come by, we can look at component datasheets easily.



The above is a power consumption over temperature plot for a processor, one of the major power consumers in your devices. Most components have a positive coefficient for power consumption and temperature. Some have less linear curves where consumption is minimum at some middle value. 

But for the most part, hotter devices use more power to operate normally. 



As others have commented, this doesn't take into account the battery capacity when it gets cold. The lower capacity of the battery due to temperature might be large enough to make the devices seem to last less time in the cold. But, the answer of "do they consume more power when cold?" is no.