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No, the snowflake + surrounding air system (close system) has higher entropy then the original water + air, but it looks more organized. This is true for the formation of any crystal in general.
The opposite would violate the 2nd law of thermodynamics
the total system of snowflake + environment has higher entropy, but the snowflake and its particles, seen as a system, are in a lower entropy state as the snowflake than not
think about it: there are way more ways to throw around H20 in general than to arrange them into a snowflake ==> snowflakes have lower entropy than fluids.
The 2nd law assumes equilibrium conditions. It can be violated in far from equilibrium conditions. Incidentally, these conditions is where order arises.
Local micro violation of 2nd law ... possible! Something I learned from @gavincrookshttps://vimeo.com/58573746
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