Buy plastic snow. This is available from any hobby shop. If you can't buy it, you can shred pieces of white plastic down to tiny bits. They don't have to be as small as real snowflakes, but they do have to be small enough to fall gently through the air.
Create or buy a snow cradle. These are sheets of muslin that are made with small holes along one side. The plastic snow is put onto the sheet and the side without the holes is folded over the plastic snow. The sides of the sheet have string ties that allow them to be either tied to something above stage or held by stagehands. The bag is shaken up and down when it's time for it to snow on stage. The faster the bag is shaken, the faster it will snow.
Use paper snow to cover the stage floor or individual props in snow. Paper snow is a very finely ground paper that is sold in hobby stores or through online prop stores. Paper snow does not look realistic when dropped, so it is not used in a snow cradle. Paper snow is sprinkled by hand onto the area that needs snow effects.