Snowflake Cut-outs:

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!