Cream shortening in a large mixing bowl; gradually add 2 cups sugar, beating well. Add eggs, one at a time, beating well after each addition.
Sift together flour, baking powder, soda, and salt in a small mixing bowl; add to creamed mixture alternately with buttermilk, beginning and ending with flour mixture. Beat well after each addition. Stir in half of grated rind and 1/8 cup orange juice, mixing well.
Drop dough by teaspoonfuls 2 inches apart onto greased cookie sheets. Bake at 375° for 10 minutes. Remove from cookie sheets, and cool on wire racks.
Combine remaining orange rind, juice, and powdered sugar in a medium mixing bowl, beating well; spread evenly over tops of cooled cookies.