My definition of Spring commencing, at the latitude of North Alabama, is when the suns declination reaches 10 degrees south, and the daily mean temperature rises back up to 50 Fahrenheit( 60 for a high and 40 for a low). Any snow, ice, or bitter cold around or after reaching this criterion during the season change would be termed a "Spring snow or Spring cold snap" as opposed to a "winter" event.
Of course someone in a more northerly latitude may not agree with this assessment because they stay much colder despite a high sun angle. And vice versa for lower latitudes.