Snow is created when the water droplets in a rain cloud are frozen (i.e. the atmosphere they are in is under 0 degrees celsius). The ground temperature only affects what TYPE of snow you get.
When it's very, very cold, (usu. 10-20 below freezing) even at ground temperature, you get small, tight snowflakes.
When it's a little warmer (i.e. a few degrees within freezing) at ground temperature, the water melts a little and expands the snowflake, making it lighter (i.e. "fluffy" snow).
If it's slightly warmer than that at ground level, you get sleet.
When there is a high pressure front in the atmosphere, but it's cold (around freezing temps) at ground level, the cloud is actually raining, but the water drops freeze shortly thereafter and you get hail.
When it's cold in the atmosphere, but not very cold at ground level, the snowflakes melt mid-fall, and you get freezing rain.
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