I have recently come from Pebble watches and they had the native feature of displaying temperature and weather conditions ( sunny cloudy rain) on their watch faces from a given zipcode. I would assume we could set it up to use the last know gps position or still uses a zipcode. Or could just pull it from the weather widget...
CIQ watchfaces are quite restricted in what they can do (it's all about the battery - it's why you can go days or weeks without charging). One of the things you can't do is any sort of comm, so getting the data from the net isn't possible.
Also, there's no way for any CIQ app to access another apps data, so it's not something you can get from the weather widget.
You can get the data in a watch-app (that could look like a watch face), as it can do comm.
