Sift together the flour, cream of tartar, baking soda and salt; set aside.
In a large bowl, cream together the sugar and oil. stir in the egg, vanilla and water; blend well. Gradually blend in the sifted ingredients. Stir in the chopped nuts last. Roll dough into 2 logs, wrap in waxed paper and chill for several hours or overnight.
Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets. Cut the dough into thin slices and place 1 to 2 inches apart onto the prepared cookie sheet.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.