Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a 9x13-inch baking dish.

Place carrots into a medium pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until carrots are just tender, about 15 minutes. Use a slotted spoon to transfer carrots to a bowl. Add zucchinis to simmering water in the pot and cook until tender, 2 to 3 minutes. Transfer zucchinis to the bowl with carrots. Drain water from the pot, reserving about 1/4 cup cooking liquid.

Add mayonnaise, onion, horseradish, salt, and black pepper to a large bowl. Stir in reserved cooking liquid. Mix carrots and zucchinis into mayonnaise mixture until well combined; pour mixture into the prepared baking dish.

Mix bread crumbs and melted butter in a small bowl until combined; sprinkle over vegetable mixture.

Bake in the preheated oven until bread crumbs are lightly browned, about 15 minutes.