Preheat oven the 375°.
In a large mixing bowl, cream together the shortening and sugar.
Beat in the pumpkin, eggs and milk.
Combine the flour, baking soda, salt, cinnamon, allspice, cloves and nutmeg; gradually add to creamed mixture.
Drop by tablespoons 2 inches apart onto a greased baking sheet.
Bake for 10-13 minutes or until lightly browned.
Remove to wire racks to cool completely.
In a small bowl, combine the frosting ingredients; beat until smooth.
Frost cooled cookies.