Sometimes the sign is used to indicate which "direction" the temperature is moving. If it was -10° overnight and it's -0° now, the puddles outside will still be frozen. If it was 10° overnight and it's 0° now, the puddles will still be liquid.
(Edit: no idea whether this applies to the Apple watch, it's just a use case for -0 with regards to temperature.)
(Edit: no idea whether this applies to the Apple watch, it's just a use case for -0 with regards to temperature.)