Sort cranberries, discarding any bruised or decayed fruit; rinse and drain berries. In a 1- to 2-quart pan over high heat, bring cranberries and 1/2 cup water to a boil. Reduce heat and simmer, uncovered, until skins pop on berries, about 10 minutes. Add sugar and stir until dissolved. Remove from heat.
Stir in 1/2 cup cold water, lemon peel, and lemon juice. In a blender, whirl half the mixture at a time until smooth. Pour purée into a 9- by 5-inch loaf pan. Freeze until solid, at least 3 hours or up to 1 week (cover when solid).
Cut cranberry ice into 1-inch cubes. With a wide spatula, lift cubes out of pan and drop three into each Champagne flute or wineglass. Pour 1/4 to 1/3 cup wine over cubes. Garnish each glass with a mint sprig and serve immediately.