For people who live in countries where there is not much snow or none at all, there is only snow and ice. Maybe we can add “frost”, the ice that forms in the early morning and usually damages crops. However, for people who live in “frozen” countries, recognizing different types of snow can be a question of life and death, literally. Therefore, people who live in countries like Greenland or within the Arctic Circle, have many more words for snow and ice, most of them may not even have a direct translation in other languages.
Snow is “rain” when temperatures are below the freezing point (0ºC). If there is no moisture, there is no snow, even when temperatures are really low. For example, in Antarctica, there are vast spaces called Death Valleys where there is no moisture, therefore, no matter how low the temperature is, there is no snow, ever. The level of moisture determines the type of snow and, ultimately, how dangerous it is. The temperature also influences as the ice crystals form differently under different temperatures. This is also true for ice, which, in a way, is a form of snow. Or better yet, snow is a form of ice. The difference is that snow is formed in air (hence, “frozen rain”) and ice is formed on the ground.
However, it is not only the level of moisture and temperature that determine the type of snow. There is also the snow that accumulates on the ground and then melts and then freezes again (hard-packed snow). The best snow for skiing is the snow that has just fallen when the weather is dry, but cold enough to freeze water (powder snow). Then, there are the types of snow that are more than one year old, but are still loose enough for skiing (firn snow). When this type of snow consolidates, it forms a glacier. Wet snow is a snow that is heavy with water, the best one for building snowmen. Drift snow is the snow that is “transported” by the wind and can cause avalanches.
Well, this is a very extensive subject. For more information, you can start by reading: