Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a 9x13-inch baking dish.
Place carrots into a pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until just tender, about 15 minutes. Strain carrots out of the water with a slotted spoon. Add zucchini slices to the pot and simmer until tender, 2 to 3 minutes. Drain, reserving about 1/4 cup cooking liquid.
Stir reserved cooking liquid into mayonnaise, onion, horseradish, salt, and black pepper in a large bowl. Mix cooked vegetables into mayonnaise mixture until well blended; pour mixture into prepare baking dish.
Mix bread crumbs and melted butter in a small bowl; sprinkle over vegetables.
Bake in preheated oven until bread crumbs are lightly browned, about 15 minutes.