I remember being stuck on a ski lift on a day that was too cold and windy for any intelligent person to be skiing. The phone in my breast pocket was cold to the touch and the battery capacity evaporated by 50%. The display's response time was hundreds of ms. I turned it off at that point.

Not a huge deal. Just charge it when it's warmer. I would have been a little surprised if something inside popped and suddenly the phone started thermal throttling or had water damage.

In my city, temperatures are regularly below -20 Celsius and sometimes below -40. iPhone just doesn't work. You need to keep it close to body and you can't use it outside for a prolonged period of time, it'll simply shut off in a few minutes and won't turn on until you heat it.

Old phones and some android phones work just fine in these conditions.