As long as there is moisture in the air and a way for it to rise and form clouds, there can be snow, even in temperatures below zero.  But very cold air doesn’t have much moisture in it, and it is also dense and heavy, so clouds don’t form unless the cold air rises up a mountainside or unless the cold air blows across a body of water and collects moisture.  Most heavy snowfalls occur in temperatures 15 degrees Fahrenheit or above.