Cold weather did not cause your problems, they just caused them to show up. The NAV screen may just be a coincidence, but these certainly DO work in cold climates. And can fail in warm climates.

I would pressure test the cooling system for starters. These cars are known for coolant and oil leaks, so it's not unusual at all; but you need to track them down, and either do the repairs yourself, or pay for some expensive repairs.

For oil, start by checking all around the valve covers. Also check the gasket on the oil filter.

For the coolant, I'd take a close look at the expansion tank first, but there are a lot of potentially leaky components in this system, (I just needed to replace the transmission thermostat on mine). There are a LOT of plastic bits that can get brittle and break, causing leaks. Not using BMW coolant with distilled water only can also lead to problems.

As far as the dead pixels, if those stay dead now that you're back in the warmth, you need to replace the screen. It's not that hard a job for a DIYer, and I just did this myself with help from a DIY thread posted here. Got the screen on eBay for $168. (eBay seller eurotech.lcd out of China) If they don't have the correct screen listed right now, just contact them directly, and they can definately supply it. They are just getting started with eBay, so they are limited in terms of how much they can list. But others here have bought from them directly. 100% plug and play.

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2014 BMW 328i Xdrive
2011 BMW 335i M-Sport
2008 BMW X5 4.8i Sport
2000 BMW 528i 5sp