Whisk the tomato juice, Worcestershire sauce, horseradish, hot sauce, parsley, 1 teaspoon pepper and 1/2 teaspoon celery salt in a large bowl. Juice half of the lemon; add to the bowl along with the olive juice.
Transfer 1 cup of the mixture to a bowl and stir in the vodka; cover and freeze until ready to serve (it will not solidify).
Pour the remaining tomato juice mixture into a baking dish, cover and freeze at least 3 hours, stirring with a fork after 30 minutes to break up any ice crystals.
When ready to serve, scrape the granita with a fork so that the texture is similar to crushed ice.
Cut the remaining lemon half into 8 wedges. Thread 2 pieces celery, 2 olives and 2 lemon wedges onto 4 skewers, alternating the garnishes.
Mix the paprika and remaining 1/2 teaspoon celery salt on a plate. Moisten the rim of 4 glasses with a damp paper towel and spin them in the seasoning to coat.
Pour some of the vodka mixture into each glass and top with the granita; garnish with the skewers and serve with a straw and spoon.
