Cutting snowflakes out of paper is a classic kids’ activity, and it's still a good one. Remember, however, there are no eight-sided or four-sided snowflakes in nature, so hold out for real six-sided crystals.
Rather than making random cuts in the folded paper, try making snowflakes that look like the real thing! That will add a challenge to the project, and require some thinking. It's more difficult than it sounds!