If you do want to try and copy a snowflake that you see, or at least get an idea of how to make one similar, try to visualize the slice of the snowflake that represents the completely folded paper. This is one slice out of twelve symmetrical slices. It will be a line that cuts through the middle of one point, and intersects with a line cut though the middle of the "valley" between it and the adjacent point. If it makes it easier, pretend that the snowflake is a clock and the lines you're imagining are the hands when it's one o'clock. See picture.
This slice of the snowflake shows what your cuts should look like if you want a snowflake that looks like this. It may be easier to visualize if you look at the black (cut out) spaces and think about those shapes being cut away.