Alex I understand what you are saying - at least I think I understand what you are saying mate
and I must admit that some days even that feat seems astounding.
I will say 2 words straight up for why no 2 snowflakes do not appear to ever be the same : Chaos Theory.
In addition though I think there are 2 ways to look at that old "adage" .... one is as indicated above (thanks Shredder), I think that if you try and find 2 identical snowflakes you might search for a thousand lifetimes and still never find an identical pair. Therefore for all
practical purposes "no 2 snowflakes are alike".
However.....
Even if the chance of finding 2 that are the same is a billion, billion, billion, billion, etc, etc, etc to 1 - even an infinitely small chance is still a chance, and in an almost infinite universe (latest update I've heard this week is 46 billion light years across - that's a lot of water and a lot of possible snowflakes) there is still therefore a potential chance of 2 snowflakes, somewhere, being the same.
Summing up:
In practice - no 2 snowflakes are the same.
In theory - it's possible, at an incredibly low possibility level.
(Douglas Adams fans fire up your Infinite Improbablility drive, we have snowflakes to check)
I hope this promotes some further deep thought. Carry on chaps.