@kagisomoleme It would be great to know how cold it gets. Either in Celsius or Fahrenheit. What you are describing sounds like a power issue. I suggest that you start off with a battery change. Batteries do not like the cold and if they are aged, they like it even less.
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Use something like [https://www.youtube.com/watch?v=ahxAzdiuSK0 |this video] to work on it.
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While you work on your battery, take lots of pictures. Once you are done with it, take those pictures and create a guide for iFixit. That will help the next person that has the same problem as you do. It's easy and fun to create these guides. https://ifixit.com/Guide/new The iFixit community will appreciate this.
@kagisomoleme It would be great to know how cold it gets. Either in Celsius or Fahrenheit. What you are describing sounds like a power issue. I suggest that you start off with a battery change. Batteries do not like the cold and if they are aged, they like it even less.