Yes. You can trigger actions before, during or after any weather event. For each condition, set the Trigger Type:
Forecast to act before the weather arrives, looking up to 7 days ahead.
Current to act while it's happening.
Past to act after it has happened, looking up to 7 days back.
For example, show ads for snow chains when snow is forecast within the next 2 days, or ads for roof repairs within 3 days after heavy rain.
See How do time frames work for weather targeting? for the full set of options.