Make soup: Melt butter in a pot over medium heat. Add onion and celery and cook, stirring, until softened and translucent, about 5 minutes. Add garlic and sauté 1 minute, then add Worcestershire sauce and sauté 1 minute longer.
Open tomato cans and cut tomatoes (still in cans) with kitchen shears into large chunks. Add tomatoes and juice to pot, along with salt and pepper. Increase heat to high and bring to a boil, then reduce to a simmer and cook 20 minutes, stirring occasionally. Remove from heat and stir in horseradish. Let soup cool 10 minutes, then puree in blender in batches and pour through a strainer into a large pan. Keep warm.
Make topping: Using an electric mixer on medium-high speed, beat cream with horseradish until it forms stiff peaks. Divide soup among 8 cups and top with a dollop of horseradish cream. Garnish with chopped chives, if desired.