Beat butter at medium speed with an electric mixer until creamy; gradually add granulated sugar and vanilla, beating well.
Combine flour, cocoa, salt, and nuts; gradually add to butter mixture, beating until blended.
Portion dough by teaspoonfuls, and roll into balls; place on ungreased baking sheets.
Bake at 350° for 8 to 10 minutes. Roll warm cookies in sifted powdered sugar.