I had a few hours to play around so I drew a design on Corel x4 and built the snowflakes out of supplies I already had.

Supplies:
Pencil/pen
Cutter (Laser Engraver / Utility knife / scissors / razor blades / etc.)
Krylon Spraypaint (white or primer and colors of your choice)
Cardboard sheets (0.108 inch)
Painter spray sheild (can be found at the local paint/hardware store)
Hot glue gun and glue sticks
String
Sandpaper (220 grit or higher)

Step 1: Transfer Design

Make a template out of paper (copy paper).
Trace onto the cardbroad using a pencil.

Step 2: Cut Outs and Dry Fit

Cut out all of the cardboard pieces (I used the Epilog Mini Legend Laser Engraver).
Do a dry assembly to ensure fit.
If needed, use sandpaper to clean/smooth the edges.

Step 3: Painting the Snowflakes

Lay out all cardboard pieces (in a well ventilated area).
Spray a white/primer undercoat using Krylon.

***To avoid having the smaller cardboard pieces from blowing around when applying the spraypaint use any extra cardboard to create an "X-Frame" to hold the smaller pieces in place.

Spray Krylon colors of your choice (the cardboard will take about 4-5 coats of paint for good coverage).
Let dry before handling (this will take a few hours).