Preheat the oven to 350 F. Line a cookie sheet with parchment paper or a silpat.
Cream the butter and powdered sugar in a stand mixer using the paddle attachment.
Add the cake flour, vanilla, and chopped nuts. Mix until ingredients are just combined.
Use your hands to roll the cookies into small balls, about the size of a bouncy ball.
Space the cookies 2" apart on the lined cookie sheet. Use a fork to gently press the cookies flat, and leave tine marks in the cookies.
Bake for 10 minutes.
Let cool to the touch. Meanwhile use a spice grinder to turn sanding sugar into powdered sugar, one color at a time.
Wipe the grinder between colors and put each color in a separate bowl.
Once cookies are cool, gently coat the cookies in whatever colored sanding sugar you want.
These cookies keep in a tightly sealed plastic container for up to a week.