Preheat oven to 350 degrees.
Measure flour, sugar, cocoa, baking soda, and salt into an 8- or 9-inch round or square baking pan and mix well. Be sure to combine all ingredients.
Make three holes in the dry mixture. Pour the vinegar into one, the oil into another, and the vanilla into the third.
Pour the cold water over the entire pan. Mix all the ingredients together until well blended.
Bake in the preheated oven for 35 minutes, or until a toothpick poked into the center comes out clean.
When finished, place cake on a wire rack and let it cool in the pan for approximately 35 minutes.
Prepare the frosting: combine confectioner's sugar and water in a ziploc bag.
When the cake is cool, remove from pan. Snip a small corner off the ziploc bag, and frost the cake as desired.