(Edit: no idea whether this applies to the Apple watch, it's just a use case for -0 with regards to temperature.)
Air temperature is commonly measured at 2m above ground. An measurement of 0° air temperature does not imply 0° ground temperature. The more significant effect is that the ground has a higher thermal capacity than the air, so it changes temperature more slowly throughout the day. If it's been colder before and now it's 0°, the ground is still way below 0° and thus puddles are frozen. If it was warmer and now the air has cooled down to 0°, the ground is going to be a bit warmer still and thus puddles are liquid.
Denoting this difference as +0° and -0° does not seem very useful since the same effect is going to be nearly equally significant at 1° or -2°.
(Sidenote: The thermal capacity of the ground is also the reason why air temperature is not measured anywhere near the ground.)
$ printf '%.0f°\n' 0.3
0°
$ printf '%.0f°\n' -0.3
-0°