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Set oven to 350 degrees F.
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Prepare ungreased baking/cookie sheet/s.
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In a large mixing bowl cream the butter with sugar until fluffy (about 3 minutes).
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Beat in molasses and water.
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In another bowl combine flour with ginger, baking soda, cinnamon, allspice and salt; add to the creamed mixture and mix until well combined.
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Cover the bowl and refrigerate for 1 to 1-1/2 hours or until easy to handle.
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Lightly flour a work surface.
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Roll out the chilled dough to 1/4-inch thickness.
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Using star-shaped cookie cutters dipped in flour (about 2-1/2 inches wide) cut out shapes.
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Place the dough stars onto prepared cookie sheet about 2-inches apart.
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Bake for about 10-12 minutes or until edges are firm.
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Remove to wire racks and cool.
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For the icing; in a bowl combine all icing ingredients until smooth and well combined.
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Transfer to a heavy small plastic bag, then cut a small hole in a corner of the bag.
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Pipe the icing around the edges of the cookies or as desired (the icing will harden upon standing).