Using a cocktail shaker, combine vodka, apple cider, and lime juice. Shake until well mixed. \tFill 2 copper mugs 3\/4 of the way full with crushed ice, then divide the cocktail mixture between mugs. Top off each mug with chilled ginger beer, filling to top. \tTop with a sprinkle of cinnamon. Garnish with cinnamon sticks and a caramel apple slice. Serve and enjoy!