For crocheters who prefer to work with yarn, instead of thread, I've compiled the following list of links to snowflake theme free crochet patterns, where the pattern example is crocheted with yarn. These patterns are at various sites around the Internet; at the beginning of the description, I give the name of the web site where the pattern is found.
At About.com Crochet (this site): A coaster with a snowflake design, large enough to be used with a large mug. There are links to a photo how-to for the 3-picot group that is used on the edge of the snowflake.
At Crochet Me: It can be worn like a circle shrug, capelet, scarf or wrap. It is crocheted with a soft worsted weight yarn.
At Art of Tangle: Crocheted in hexagon motifs, using a light worsted weight yarn.
At Priscilla's Crochet Patterns: Crocheted with worsted weight yarn or speed-cro-sheen.
At Priscilla's Crochet Patterns: Crocheted with cotton worsted weight yarn.
At Priscilla's Crochet Patterns: The white snowflake motif stands out against a darker color background. Crocheted with cotton worsted weight yarn.
At Dayna's Crochet - She wrote the directions for these easy snowflakes with mix-and-match choices for the different rounds, along with photos of some of the possible combinations.
At Crochet Memories: Crocheted with Caron Christmas Glitter yarn.