Step 1: Prepare your glasses by moistening the rim with a lemon wedge or water, then dipping into white sanding sugar to create a festive sugared rim. Set aside.
Step 2: In a large pitcher or punch bowl, combine the cranberry juice, pomegranate juice, pineapple juice, coconut milk or cream, and peppermint extract. Stir well to combine.
Step 3: If desired, add a few drops of red food coloring to enhance the punch's vibrant color. Stir gently.
Step 4: Just before serving, add the lemon-lime soda or sparkling water to the juice mixture. Stir gently to incorporate without losing too much fizz.
Step 5: Add plenty of ice cubes or crushed ice to the punch bowl or individual glasses. Ladle the punch into the prepared glasses.
Step 6: Garnish each serving with a candy cane for stirring, and optionally top with whipped cream or mini marshmallows.