Pre-heat the oven to 350°F.
Make the cookies: sift the flour, baking powder and salt into a small bowl. In a large bowl, cream the butter with the sugar until fluffy. Beat in the egg, followed by the chocolate and vanilla. Stir in the flour mixture, half at a time, blending well to make a stiff dough.
Roll the dough, a rounded teaspoonful at a time, into a ball between the palms of your hands. Place the balls 1 inch apart on lightly greased cookie sheets.
Bake for 12 minutes, or until firm. Remove the balls from the cookie sheets; cool completely on wire racks.
Now make the snow glaze: mix 3 cups confectioners’ sugar with 3 tablespoons water and 1/2 teaspoon vanilla in medium size bowl; beat until smooth. If the glaze gets too thick while frosting the cookies, add a drop or two of water and beat again until smooth. These ingredients will make about 1 cup of glaze.
When ready to frost, place the balls about 1 inch apart on wire racks set on waxed paper or foil to catch any excess frosting. Spoon the glaze over the balls to cover them completely; let set slightly. Scrape any frosting that drips onto the waxed paper or foil back into the bowl; stir well. Spoon another layer over the balls to make a thick coating; let stand until firm.
Alternatively, roll the baked cookie balls while still warm in finely chopped walnuts or in granulated sugar to give an icy effect.