According to Environment Canada to produce snow, the air must hold at least some moisture in gaseous form. The water vapor must be cooled beyond the freezing point at which snow crystals form.

Because warm air holds more moisture than colder air, the heaviest snowfalls and large flakes occur at temperatures close to freezing. As the air becomes colder the flakes become finer and finer.

It is never too cold to snow (even when it got as cold as -81 Fahrenheit in Snag, Yukon, back in 1947), but the amount of snowfall is usually less the colder it is. If that's any consolation.