I disabled the alerts on iPhone by going into Notifications settings, scrolling to the bottom and toggling the Amber Alerts and Emergency Alerts off. This is on an AT&T phone, not sure if it's carrier-specific.

A friend of mine experienced a similar thing before my phone had the capability. His phone went crazy with a "blizzard warning", even though there were no storms around, and I don't believe the NWS has ever issued a blizzard warning for this area.