It’s hard to say for certain since it rarely gets that cold in the UK, and I’ve only had the lock for a few months. However, I would assume the emergency key would work. The physical key operates the latches that secure into the door frame, so as long as they’re lubricated, the key should function properly.
Additionally, the key is inserted from underneath the handle, which helps prevent water ingress if mounted correctly. Ultimately, it depends on the type of grease used; if it doesn’t freeze at -10°C, it should still operate effectively.