Now that I've completed my six snowflakes both with and without doodads, I can state with confidence that I much prefer the ones with the doodads. Those little metal links add just enough weight to the snowflakes to let them hang nicely. I also think that the findings help the snowflakes hold their shapes better.
So, pattern #6...
size 20 Lizbeth, Christmas Delight #116
2 shuttles wound CTM
Pewter Flower from Fire Mountain Gems, stock #H20-9117FY
*Ring: 4 - 4 + 4 - 4 (if tatting without doodad, make the join a picot); do not reverse work; switch shuttles
Chain 8; reverse work
Ring: 4 - 4 - 4 - 4
Ring: 4 + 4 - 2 - 2 - 4 - 4
Ring: 4 + 4 - 4 - 4; reverse work
Chain 8; do not reverse work; switch shuttles
Repeat from * 5 times.
Remember that on the last center ring, the final picot should be a join to the first picot of the first ring.