Most snowflakes have hexagonal symmetry, which means that there are six lines you could draw through the center where one side would be the mirror image of the other. (Or six ways you could fold it so the sides would overlap each other.) Try it out on any of the snowflakes in the picture! Three of these lines will be along the "arms" of the snowflake, and three will be between the "arms." Check out some more beautiful photographs of single snowflakes here and look for the lines of symmetry in each flake.
Follow this link to learn how to make paper snowflakes of your own that actually have hexagonal symmetry. You can use any piece of square paper to start, but origami paper is perfect for this one since it's a great size and usually has a white side and a colorful side. (If you don't have the supplies or you're not feeling crafty, you can even design a virtual snowflake here.)
Once you've gotten the process down, challenge yourself! Can you picture or sketch the snowflake you want to make, then fold and cut to make it happen? Can you fold and cut, then draw a prediction of what your snowflake will look like before you open it?
Like all good scientists, doing one experiment might just make you ask more questions. Here are some questions you might have, and a good place to find the answers:
Do all snowflakes have hexagonal symmetry, or are there other types? Answer here.
Does artificially-made snow have hexagonal symmetry and pretty snowflakes? Answer here, then scroll down to "Artificial Snow."
Why are snowflakes symmetrical anyway? And how do the arms "know" how to match each other? Answer (sort of) here.