Is it permissible to move snow on Shabbat, or does snow have the status of "Muktzeh" (items that are forbidden to be handled on Shabbat)? For example, may one brush snow of his coat on Shabbat, or move snow off a railing that he wishes to use?
The Mishna Berura (commentary to the Shulchan Aruch by Rabbi Yisrael Meir Kagan, the "Chafetz Chayim," Lithuania, 1835-1933) writes (338:30) that rain that falls on Shabbat does not have the status of "Muktzeh" or of "Nolad" (objects that came into existence on Shabbat and may therefore not be handled until after Shabbat). Chacham Ovadia Yosef extended this ruling to apply to snow, as well, which is, essentially, a frozen form of rain, and he thus allowed moving snow on Shabbat even directly with one's hands. This is the position as well of several other prominent authorities, including Rabbi Tzvi Pesach Frank (Jerusalem, 1873-1961) and Rabbi Shlomo Zalman Auerbach (Jerusalem, 1910-1995), as cited in the work "Shemirat Shabbat Ke'hilchata" (classic digest of Shabbat laws by Rabbi Yehoshua Neubert, a disciple of Rabbi Auerbach).
Although Rabbi Moshe Feinstein (Russia-New York, 1895-1986) ruled that snow on Shabbat has the status of "Nolad" and may not be moved, we follow the authorities mentioned above who permit moving snow on Shabbat.
May one make a snowball or snowman on Shabbat?
Rabbi Shlomo Zalman Auerbach ruled that making snowballs or snowmen, which involves bringing together different components to form a single entity, is forbidden on Shabbat, due to the resemblance to "Boneh," building, one of the areas of forbidden activity on Shabbat. One may, however, throw snowballs that had been prepared before Shabbat (in an area surrounded by a valid Eruv), and we do not consider the dissolution of the snowball on impact as "Soter" ("dismantling," one of the areas of forbidden activity on Shabbat).
Summary: One may move snow on Shabbat, even directly with his hands, but one may not make a snowball or snowman on Shabbat. It is permissible to throw a snowball that had been made before Shabbat (in an area surrounded by a valid Eruv), even if it will inevitably break as a result.