Cream the butter and sugar. In a large mixing bowl, beat the softened butter and powdered sugar with a hand mixer until light and fluffy. Scrape down the sides of the bowl as needed.
Add the vanilla. Mix in the vanilla extract until combined.
Finish the dough. Add the flour and salt. Mix on low speed just until incorporated, then mix in the ground walnuts until evenly distributed. Use a spatula to bring the dough together without overmixing.
Chill. Cover the bowl and refrigerate for 30 minutes.
Prepare the oven and baking sheet. Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Shape the cookies. Using a tablespoon as a guide, divide the dough into 28 portions and gently roll each into a ball. Arrange on the prepared baking sheet, leaving approximately 2 inches between cookies.
Bake. Bake for approximately 15 minutes, until the cookies are set and the bottoms are lightly golden. The tops should remain pale.
Rest briefly. Let the cookies cool on the baking sheet for 5–10 minutes. They should still be warm but firm enough to handle gently.
Add the first coating. Place the coating sugar in a bowl. Carefully roll each warm cookie in powdered sugar, coating all sides. Handle gently, as the cookies are fragile while warm. Set on a wire rack or parchment-lined tray to cool completely.
Coat again. Once completely cool, roll the cookies in powdered sugar a second time for a snowy finish.