Snow is made of frozen water droplets that are shaped like ice crystals. They stick to the ground if there is moisture in them -- such as from dew or rain. But once all that moisture evaporates from a snowflake or it melts away, it won’t stick to anything. It’s not the temperature that determines whether it will snow or not, but how much moisture is in the air and how the air is moving.
For it to be snow, the temperature needs to be below freezing all the way from the surface down to the clouds where the snowflakes form. However, the temperature in the sky can vary from location to location because of terrain. It can also be warmer up there than it is down near the ground, if a layer of warm air is stuck above the snowpack. If that layer is warm enough, it will melt the snow to sleet or rain before it can make its way down to the ground.
This process is why you sometimes see rain or sleet that never makes it to the ground because it melts as it falls through the air and then re-freezes on contact with hard surfaces. Eventually the slushy precipitation gets to be too warm and turns back into a liquid (like water or juice). However, it is possible for cold, dry air to bring snow down without that melt-and-refreeze process happening. That’s the type of snowfall that you can often find in blizzard conditions.