Of course it is. Weather Forecast doesn't collect any personal information. Therefore, nothing is sent to external servers and no info is stored in your device.
Then, why do we ask for some critical permissions?
- Network communication: data need to be downloaded.
- Your location: in case you use geolocation.
- Phone state: we need to read phone state so we can automatically update widgets after booting when detecting an Internet connection (TelephonyManager).
- System tools: change Wi-Fi state in case you use the switch available on widget 4x1.