Snow forms only when the temperature in the atmosphere is at least 32 degrees Fahrenheit and the air has at least a bit of moisture. In general, snow does not occur if ground temperatures are at least 41 degrees Fahrenheit.
In some conditions, snow can reach the ground if ground temperatures are above 32 degrees Fahrenheit as long as they are under 41 degrees Fahrenheit. While temperatures can be too high for snow to occur, temperatures are never too cold for snow to be possible as long as the air has some moisture, and there is a mechanism to cool or lift air. In general, however, heavy snow is most likely to occur when air near the ground is a relatively warm 15 degrees Fahrenheit, because warm air retains more water vapor.
The Dry Valley areas in Antarctica are examples of locations that are extremely cold but do not get much snow. This is because the air there does not have enough moisture for snow to fall frequently, and severe winds remove much of the remaining atmospheric moisture.
Irregular and large snowflakes are most likely to form in temperatures closest to 32 degrees Fahrenheit with light wind and erratic conditions. Those snowflakes can measure as much as 2 inches in diameter.