In a large mixing bowl, cream the softened butter with the powdered sugar until light and fluffy—about 2–3 minutes. Mix in the vanilla extract.
Gradually add the flour and salt to the butter mixture, stirring until just combined. Fold in the chopped nuts until evenly distributed. The dough will be thick and slightly crumbly but should hold together when pressed.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper. Scoop out tablespoon-sized portions of dough and roll into balls. Place about 1 inch apart on the baking sheets. Bake for 12–14 minutes, or until the bottoms are lightly golden but the tops remain pale.
Allow cookies to cool for 5–10 minutes. While still warm, roll each cookie in powdered sugar until fully coated. For a snowy finish, roll them again once completely cooled.