Prepare the Dough - In a large mixing bowl, cream together the softened butter and powdered sugar until light and fluffy. Add vanilla extract and mix well. Gradually incorporate the all-purpose flour, mixing until just combined. Fold in the finely chopped pecans until evenly distributed throughout the dough.
Shape and Bake - Preheat your oven to 400°F and line baking sheets with parchment paper. Using your hands, roll the dough into 1-inch balls and place them about 1 inch apart on the prepared baking sheets. Bake for 13-15 minutes until the bottoms are lightly golden but the cookies remain pale on top.
Sugar Coating - While the cookies are still warm, gently roll them in powdered sugar, coating completely. Place on a wire rack to cool. Once completely cooled, roll the cookies in powdered sugar a second time for that classic snowball appearance and extra sweetness.