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The head unit as you call it as actually called the ACM (Audio Control Module) and it does need to be program to the vehicle because it is actually a module that communicates with several other modules in the vehicle. It needs to configured and programed so it will work properly. It needs to be done with a scan tool connected to the internet to properly program it to the vehicle and other modules.
I live in Florida and we deal with heat, not much cold weather. But we have seen modules fail after a battery is replaced. Ford will not give us internal details on the modules. We have seen the Master Reset fix problems temporarily. We have even seen network issues. Which is the wired network between all the modules in the vehicle so all the modules can share information on vehicle operation.