I use spray starch, you can get it powder form too. If you use the powder, mix it with some water and dab the starch on your snowflake. You can let it dry and if you need it stiffer, re-apply. The good thing about starch is, it doesn't colour you whites and doesn't leave a white stain on your colours.
I have used it to starch some crochet snowflakes, and always use it for my tatting.