The beautiful origami snowflakes in the picture above were designed by Toshikazu Kawasaki. The diagrams are available in his book Greatest Dream Origami (ISBN 9784255005058).
I like them because they are three dimensional and quite easy to fold. My favorite is the one at the bottom right of the picture, that looks almost like a flower.
I would recommend to use very thin paper. I folded the snowflakes with hexagons cut from 9" (225 mm) squares of Pacon Paper Squares and 6"(150 mm) squares of Thin Crisp Washi Paper.