Prepare the Dough. In a large mixing bowl, beat the butter and ½ cup powdered sugar until creamy. Mix in the vanilla extract. Gradually add the flour and salt, blending until a dough forms. Stir in the finely chopped nuts.
Chill the Dough. Cover the dough with plastic wrap and chill for 30 minutes. This step ensures the cookies hold their shape while baking.
Shape the Cookies. Preheat your oven to 350°F and line a baking sheet with parchment paper. Roll the dough into 1-inch balls and place them on the baking sheet, spacing them slightly apart.
Bake. Bake the cookies for 12-14 minutes or until the bottoms are lightly golden. Allow them to cool for 5 minutes on the baking sheet.
Roll in Powdered Sugar. While still warm, roll the cookies in powdered sugar. Once fully cooled, roll them again for a thick, snowy coating.