Starting from a clean scene in overhead view, Add a Circle (Shift-A) with 12 verts (F6 and change verts)
Extrude the circle with scaling in (E then S) a couple times then merge the inner most circle at the center (W->Merge->At Center).
Extrude the top 3 verts constrained along the Y axis (MMB during extrude)
In face select mode, select half of the extruded part and where it is connected to the circle, invert the selection (ctrl-I), and delete faces (X->Faces)
Reselect the mesh and Add a mirror modifier from the properties panel, enable clipping
Add an Empty at the origin of your mesh.
Also add an array modifier, uncheck "relative offset", select object offset and set it to the empty. This will allow us to have an arbitrary rotation. Since snowflakes have 6 sides, set the Count to 6. Also Enable "Merge" and "First Last".
You should now have a base for an editable radially symmetrical snowflake.
Duplicate the Mesh and Empty and edit the new mesh. The only place you need to be careful is in the center.
When you are satisfied with the snowflake, apply the modifiers in the modifier panel.
For my project, I created several of these and put them in a group. Then used that group as a dupligroup for a particle system. From a distance I think it played pretty well. You can of course add a solidify modifier or continue to tweak them to your liking.