Prepare the oven.
Preheat the oven to 350°F. Line a baking sheet with parchment paper.
Mix the butter and sugar.
In a bowl, beat the softened butter and 1/4 cup powdered sugar until smooth and well combined.
Make the dough.
Add the flour and finely chopped nuts. Mix gently until the dough comes together, scraping down the bowl as needed.
Shape the cookies.
Roll the dough into small balls, about 1 inch across, and arrange on the prepared baking sheet with a little space between them.
Bake.
Bake for 20–25 minutes, until the bottoms are lightly golden and the tops are set but still pale. Begin checking around 15 minutes if your cookies are especially small or your oven runs hot.
Roll in powdered sugar.
Let the cookies cool on the tray for about 5 minutes, until warm and firm enough to handle.
Place the remaining 1/2 cup powdered sugar in a shallow bowl. Gently roll the warm cookies in the sugar, then transfer to a wire rack.
Cool and coat again.
Let cool completely. Roll in powdered sugar a second time for a fuller, snowy coating, then serve.