Now here's a neat idea. Have a weather application that monitors the forecast and alerts you if any paremeters in said forecast exceed the numbers beyond which you'd like to be notified. For example, if the temperature is likely to get below freezing or above 30ºC or it's scheduled to rain above a certain intensity. That sort of thing. And Weather Notify has you covered, with masses of flexibility - for a few dollars of in app purchases, naturally!

From the Store description:

Never worry about checking the weather again! Weather Notify can alert you in the morning if it will rain or be excessively cold today.

Let Weather Notify keep track of the weather so you don't have to!

Get Windows Notifications to alert you of weather conditions you care about.

• Supports Both Metric and Imperial Measurements
• Live Tile Support for Predicted Conditions
• Schedule Weather Notifications

Here's Weather Notify in action:

For free you get the live tile and temperature warnings, for example here (right, in the promo shot) a toast/pop-up is arriving to warn of very high temperatures. 

The various in app purchases - it depends what aspects of the weather that you're most interested in and what you want to be alerted about!

A neat idea and one that leverages the live tile and toast notification system in Windows Phone/Windows 10 Mobile really well. You can grab this for free in the Store, and then there are in app purchases for the various extras, if you need them, as shown above.