In a large bowl of your electric mixer, cream butter, powdered sugar, and vanilla extract until light and fluffy.
Sift in flour and salt; stir until well mixed. Mix in nuts. Cover bowl with plastic wrap and refrigerate 1 hour or overnight.
Preheat oven to 400 degrees F.
Roll dough into 1-inch balls.
Tip: A small ice cream scoop is ideal for making uniform-sized cookies.
Place dough balls onto ungreased cookie sheets with about 1-inch of space between them. Bake 10 to 12 minutes or until set but not brown.
Remove from oven and cool slightly on wire cooling racks.
While cookies are baking, place the powdered sugar in a shallow dish. While still warm, roll cookies in powdered sugar until completely coated.
When cookies have cooled, roll them again in the confectioners sugar to give them a nice even coating of sugar.
The first rolling allows the sugar to melt into the cookies - the second rolling
gives the finished snowy-white topping.
Store in an airtight container.
Variation: Substitute 1 cup miniature semisweet chocolate chips for the nuts.
Yields 3 1/2 to 4 dozen cookies.