Snow flurries refers to light snowfall with no accumulation on the ground, and snow showers is the term used to describe light to moderate snowfall where a small amount of accumulation is possible. A snow shower starts and stops suddenly and snow flurries can fall on and off all day.
The amount of snowfall an area receives relies heavily on the temperature in the atmosphere. When that temperature dips to 32 degrees Fahrenheit or below, and there is moisture in the air, snow will fall. How much snow reaches the ground depends on the ground temperature. If the ground is at or below 32 degrees, the snowflakes will make it to the ground and accumulation is possible. If the ground and surrounding air is warmer than 32 degrees, the snow may still fall, but will melt the closer it gets to the ground. Generally, it will not snow if the temperature on the ground is 41 degrees Fahrenheit or above.
There is no temperature that is too cold for snow to fall. Warmer air holds more water vapor, so the warmer the ground, the more snow will fall. However, no matter the temperature, if the air is dry, there will not be snow, no matter how cold it gets.