Aiphone video door station in cold weather

I'd check with the manufacturer but I'm guessing that the only thing that would happen is that during the really cold weather, the unit would simply, "slowwwww down".

I wouldn't mount it in a highly exposed location, (direct exposure to water, ice, snow) if at all possible and you should make sure that you weather proofed it as much as possible with insulation and sealing to avoid condensation.

In my experience, cold doesn't destroy moisture protected solid state devices ..... but may cause them to become sluggish or temporarally stop working.