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PORTION sherbet into 12 (3-Tbsp.) scoops on waxed paper-covered rimmed baking sheet; press 1 cherry into center of each. Freeze 2 hours.
MEANWHILE, add juice cocktail and water to drink mix in plastic or glass pitcher; stir until mix is dissolved. Refrigerate until ready to serve.
POUR prepared drink into punch bowl when ready to serve; stir in ginger ale. Insert 2 mint leaves into each sherbet scoop for the reindeer's ears. Transfer 1 sherbet scoop to each glass of punch just before serving.