Place 3 tablespoons celery salt in a thin layer in a small dish or shallow bowl. Take empty serving glasses and moisten their rims with a lime wedge. Dip rims in celery salt to coat. Shake off excess.
In a pitcher, mix lime juice, Clamato juice, Worcestershire, hot pepper sauce, pepper, remaining celery salt, horseradish and vodka. Stir. Pour into glasses over ice.