In a saucepan, cook carrots just until crisp-tender; drain, reserving 1/4 cup cooking liquid. Place carrots in a 1-1/2 quart baking dish. Combine mayonnaise, onion, horseradish and reserved cooking liquid. Spread evenly over carrots. Sprinkle with cheese; top with bread crumbs.
Bake, uncovered, at 350 degrees for 30 minutes.