Preheat oven to 375°F. Beat the butter, icing sugar and vanilla in a large bowl until light. Add the flour, salt and nuts and stir until blended - you may need to use your hands.
Roll dough into balls and place on an ungreased cookie sheet. Bake until pale golden around the edges and on the bottom. While still warm, roll in a shallow dish of icing sugar to coat. Cool on a wire rack.