Snow is commonly formed when water vapor changes directly to ice without first becoming a liquid, this process is known as deposition.
When temperatures of less than 32°F are at the higher altitude in the atmosphere the ice crystals are created.
The snow flakes are able to stay frozen as they fall because the temperatures stay below 32°F either all the way to the ground or very close to the ground.
Yes it is possible that when you step out the door and it's snowing, the temperature might be above freezing. In fact in some cases, the temperature might be as warm as 40°F. You might be wondering how is it possible that it's above freezing and it's still snowing. Well the simple answer is, as long as there's just a very shallow layer of air above freezing right at the ground, if the rest of the column of air going up in the atmosphere is below freezing, then the snowflake will melt of course as it enters the shallow warm layer, but it won't completely melt.