Preheat oven to 375 degrees F (190 degrees C). Lightly grease baking sheets.
Cream the shortening and brown sugar together until light. Beat in the eggs and vanilla. Combine the flour, 3 tablespoons drink mix, baking powder, and salt. Dissolve the baking soda into the buttermilk. Stir in the flour mixture alternately with the buttermilk mixture. Stir in the white chocolate chips. Drop dough by teaspoonfuls onto prepared cookie sheets.
Bake for 10 to 12 minutes. Frost cookies while still hot with orange glaze.
In a small bowl, blend together the butter, 3 tablespoons orange drink mix, and confectioners sugar until smooth. Mix in water 2 teaspoons at a time until a pourable consistency is reached. Drizzle or brush onto cookies while still warm.