Using an electric mixer, beat together the butter and powdered sugar until creamy.Add the salt and almond extract, and beat until incorporated, scraping down the sides of the bowl as needed.
Add the flour and walnuts and beat on low speed until combined. Chill dough in the refrigerator for at least 2 hours, until easy to handle.Preheat oven to 350 degrees F. Line baking sheets with parchment paper.
Roll dough into 1-inch balls and place on prepared baking sheets. Bake for 10-12 minutes, until lightly golden on the bottom.Let cool for 5 minutes, then roll warm cookies in powdered sugar.