Battery doesn't last, worse when cold!

Batteries generally perform better when warm & worse when cold, but I wasn't expecting it to die so suddenly when exposed to cold.

Whilst it's still lasting a few hours, spray some freeze-it spray (available readily from shops like Jaycar), onto a section of the board to try to simulate the cold to see if you get the same effect. Try a different section of the board after it recovers each time to see where the problem lies exactly.

If it was me, I'd replace the battery with a pack I can make from cheap, common batteries, just like they showed us in our country's only Electronics Magazine, Silicon Chip some years ago. I may be able to look up the article, if you wish.

Ah! I should have read your initial post more closely...

You've had the phone for 1.5 years & six months after you got it (new or second-hand?), it started giving problems. I guess you've heard about Apple's new laptops which explode when you (or anyone who's not an authorized Apple repair centre), try to change the battery? That's what it has come down to. It's built that way because they want you to buy a new one at least every year! The idea is nothing new. Back in the 1950's it was known as "pre-planned obsolescence". Apple have just taken it to the next level. When I was a technician (17 years experience there - same company!), we used to joke about building a "warranty clock" into each job we did - after 13 months, the same item'd return & we'd always have work to do!

If it were me, I'd boycott the lot of them (I own a dinosaur mobile phone myself! Completely cheaply repairable!). If you talk to only a few contacts, consider buying a UHF radio, which will pay for itself twice over at least in a year. If you're into texting, you can do this for free from ad-supported sites at your local library or from a desktop or laptop.