Preheat oven to 325 degrees F.
In a large bowl, cream together shortening, water and sugars.
Add eggs one at a time, beating well after each one.
Add molasses and vanilla.
In a separate bowl, combine flour, ginger, baking soda, cinnamon, cloves and salt.
Add dry ingredients to wet mixture and stir until combined.
Roll dough into 1-inch balls and place on ungreased baking sheets.
Bake for 12-15 minutes or until cookies are set up; let cool completely.
To make the frosting, beat shortening in a large bowl until light and fluffy.
Beat in eggnog, vanilla extract and powdered sugar until light and fluffy.
Spread on cooled cookies and serve.