In a nutshell, no. Snow can fall even at extremely cold temperatures, although the quality of the snow changes as the temperature plunges. When it gets really, really cold out -- around -40 °F or colder -- the air can be too cold to hold enough water vapor to create snow. But under ordinary weather conditions, snow can fall no matter how low the thermometer drops. Read a bit more about whether (weather?) it can be too cold to snow.
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