Preheat the oven to 375 degrees F (190 degrees C).
Place carrots in a pot and add water to cover. Bring to a boil. Reduce heat to a simmer and cook until tender, 6 to 8 minutes. Drain carrots, reserving 1/4 cup of the cooking liquid. Transfer carrots to a shallow baking dish.
Mix reserved cooking water, mayonnaise, onion, horseradish, salt, and pepper together in a small bowl until combined; pour over carrots.
Bake in the preheated oven for 15 minutes.
Meanwhile, toss bread crumbs in melted butter. Sprinkle over carrots and bake until crumb topping is crisp, an additional 3 to 5 minutes.