A. Without an “Eruv” there’s no carrying outdoors on Shabbos, and throwing is including in carrying, so that would be out. Even within a permissible carrying place, there are some issues with snowball making. Most Rabbinic sources consider intentionally compacting snow to “strengthening its composition” and related to the prohibition of building. Some go as far to say that snow which falls on Shabbos falls under the category of Muktzah.
