New York and Pennsylvania had a Nor’easter dumped on them this month. Yes, this month. In April:
Ridiculous. Not the video, just the snow.
Generally speaking, electronics can handle cold-to-hot (meaning cold and not freezing-to-hot) fairly well, but with hot-to-cold, the problem you’ll encounter more often than not are "stiff" power connectors for those chargers that are on the small side.
If you leave a cell phone plugged in overnight and the ambient temperature in the room where the phone is, such as a garage, has dropped 20 degrees from 60F to 40F (or from 15.6C to 4.4C for you metric types), when you go to pull the charger plug out, it will feel stiffer than usual.
If you go to plug in a charger to a cell phone where both the charger and phone have gone more-than-normally cold over the night, the same thing happens if you have a flat-style plug; it will be noticeably more difficult to get the charger plug into the phone’s port.
What about the screen?
Whether a featurephone or smartphone, operating the screen should never be an issue even with sudden temperature changes. Featurephones are well known to work in almost any temperature, and smartphones have glass that can withstand just about anything (except being sat on, ironically enough).
What about buttons?
It’s highly unlikely that a sudden temperature change would affect mechanical buttons (as in the non-touchscreen kind) at all. If they go cold, the worst that could happen is that they’ll feel slightly stiffer.
What should you do to avoid causing damage?
Either wait for the phone and charger to reach room temperature first before plugging in/out, or if you’re in a rush, mind the fact it’s colder and be more gentle with the plug than usual.
Do not do that "hold the phone/charger in front of a car vent at full-blast heat" thing. That does more harm than good. If you need to heat up the charger/phone quickly, put it in your pocket instead and let your body heat do the job.
If you’re one of those unfortunate souls still using an old cell phone charger that has exposed pins on the plug, definitely wait until it reaches room temperature before using it, because those pins break almost too easily when on the colder side.
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