Simple mathematics however, dictates that there are only a certain number of shapes possible for a given volume... that means it's a large but finite number of possible snowflakes, even molecularly speaking, even for star shaped snowflakes. As long as 1 more snowflake falls than the total number of possibilities between both types, then there MUST have been two identical snowflakes. Now since snow is constantly falling somewhere on earth, to the tune of anywhere from a million to a few trillion flakes per second (possibly more at times), and that the earth is pretty darn old, and will continue to exist for a long time to come... I think it's far more likely that there's been more snowflakes that have fallen than there are possible shapes.
That's purely speculation though.