Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In the bowl of a stand mixer or with an electric mixer, beat the softened butter, powdered sugar, and vanilla until smooth and creamy. Add the flour and salt and mix on low until combined. The dough may look crumbly at first, but it should hold together when pressed.
Mix in the finely chopped pecans just until evenly distributed.
Cover the dough and refrigerate for 30 minutes. This makes the dough easier to roll and helps the cookies keep their round shape.
Scoop about 1 tablespoon of dough for each cookie and gently roll into balls. Place on the prepared baking sheet.
Bake for 14 to 15 minutes, or until the bottoms are just lightly golden and the tops are still pale. Do not overbake.
Let the cookies cool on the baking sheet for about 5 minutes, then gently roll the warm cookies in powdered sugar.
Transfer to a wire rack and cool completely. Roll the cookies in powdered sugar again for a thick, snowy finish.