In a food processor, pulse together the flour, walnuts, powdered sugar, and salt until walnuts are finely ground.
Cut vegan butter into small chunks and add to flour mixture. Pulse to combine. Add vanilla and blend till dough comes together. Turn dough out onto a piece of plastic wrap, wrap tightly and chill for about an hour, until firm. This helps to relax the gluten and make the cookies tender, not tough.
Remove dough from the refrigerator. Preheat oven to 350ºF. Line two baking trays with parchment paper. Use a tablespoon to portion dough and roll into 1-inch balls and place on baking trays, 1 inch apart. Bake for 12 to 15 minutes, or until the tops are just barely turning lightly golden in color. Remove from the oven.
Sift some powdered sugar onto a large plate or wide bowl and add in colored sugar, mix together. While the cookies are still warm, roll them in powdered sugar and set aside to cool completely. Roll in sugar a second time and serve.