Using an electric mixer at low speed, cream the sugar and butter until thoroughly combined. Add the eggs and molasses and mix until combined. Sift together the flour, ginger, baking soda, cinnamon, nutmeg, and salt. Add the dry ingredients to the butter mixture and combine with a spoon or spatula.
Remove the dough from the bowl and wrap in plastic wrap; place in the refrigerator until firm, about 1 hour.
Preheat the oven to 350 degrees F.
Line cookie sheets with parchment paper. Allow the dough to sit at room temperature for about 15 minutes, until pliable. Take about 1/2 cup of dough at a time and roll onto a floured board until about 1/8-inch thick. Cut out with gingerbread boy and girl cookie cutters. You can re-roll the scraps. Using a spatula, transfer the cookies from the board to the prepared cookie sheets.
Bake for 10 minutes, until just beginning to brown at the edges. Transfer to wire racks to cool.
To make the icing, combine the confectioners' sugar and milk. Divide the mixture into thirds; leave 1/3 white, and color 1/3 green and the final third red. Decorate piping eyes, mouths, buttons, and bow ties.