Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream the softened butter and 1/2 cup of powdered sugar together until smooth and fluffy.
Stir in the vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the butter mixture, mixing until just combined. Be careful not to overmix the dough.
Gently fold in the finely chopped pecans, making sure they are evenly distributed throughout the dough.
Take small portions of the dough and shape them into 1-inch balls. Place the balls on the prepared baking sheet, leaving a little space between each cookie.
Bake the pecan balls in the preheated oven for about 12-15 minutes or until they are slightly golden on the bottom. The cookies should still be pale on top.
Remove the cookies from the oven and allow them to cool on the baking sheet for a few minutes.
While the cookies are still warm, roll them in powdered sugar until they are fully coated. You can either do this by gently tossing them in a bowl with powdered sugar or rolling them in powdered sugar one by one.
Once coated, transfer the pecan ball cookies to a wire rack to cool completely. As they cool, the powdered sugar coating will set.
Once the cookies have cooled completely, you can give them a second coating of powdered sugar if desired, for an extra snowy appearance!