Prepare the Dough:**

- In a large bowl, beat the softened butter and ½ cup powdered sugar together until light and fluffy.

- Mix in the vanilla extract.

- Gradually add the flour and salt, mixing until combined. The dough will be thick.

- Stir in the finely chopped nuts until evenly distributed.

**Chill the Dough:**

- Cover the dough with plastic wrap and refrigerate for at least 30 minutes to make it easier to handle.

**Form the Cookies:**

- Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

- Roll the chilled dough into 1-inch balls and place them on the prepared baking sheet, spacing them about 2 inches apart.

**Bake the Cookies:**

- Bake the cookies for 12-15 minutes, or until the bottoms are lightly golden. The tops of the cookies should remain pale.

- Remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes.

**Roll in Powdered Sugar:**

- While the cookies are still warm, roll them in powdered sugar until they are completely coated.

- Place the cookies on a wire rack to cool completely.

- For a snowier effect, roll the cookies in powdered sugar a second time once they have cooled.

**Serve and Store:**

- Serve the Snowball Cookies on a festive platter, or store them in an airtight container for up to a week. They also freeze well for longer storage.