It is a fact that when it snows the feeling of cold decreases. Far from being just a mere sensation, it is a real fact, the temperature rises, that's why it's not so cold, because it really doesn't. How can it happen if it snows precisely when it is cold? Let's put some perspective on the matter first.
When ice or snow melts, heat needs to be added to the system. That is, the heat that is integrated causes the temperature to rise and the water goes from a solid to a liquid state. Now, the reverse process, that of changing water from a liquid to a solid state, must release heat from the system. The "heat" of that water in a liquid state is released, leaving the water in a solid state. Thus, excess heat must be dislodged and out of the system, and it is at that moment that doing so increases the temperature while it's snowing. This is important, only when the process is happening, because once the heat is released and the snow stops, the cold will prevail, and it is when the snow stops that the temperatures will drop.
Counterintuitive right? Looking at it in more depth
When the environment is below 0ºC, we have the threshold where the water can begin to freeze. But, to form a snowflake, the heat energy given off is equal to 80 calories for each. As that heat is not concentrated, it dissipates with the rest of the cold air. When it happens with millions of snowflakes, it causes a rise in temperatures. Curious right?
When it's really cold, it's harder for it to snow if you've already done it Besides. If there is a significant drop in temperatures, snow is more likely to form, which comes largely from water vapor. But if it has already snowed, the water vapor has turned into snow. Therefore, when it is very cold, the water vapor contained in the atmosphere is either very low or practically non-existent.