Beat butter and sugar until creamy. Add salt, vanilla, flour, and nuts. Mix well. Shape dough into 1" balls. Place on ungreased pan. Bake in 375 degree F oven for 12 minutes until light brown.
Roll in powdered sugar, let cool, roll again. The powdered sugar will form a sort of frosting when it melts onto the warm cookies, but they should also be covered in powdered sugar when they are done. Consider storing them in a bag with some extra powdered sugar.