Preheat oven to 350°. Place 1 in. of water in a large saucepan; add carrots. Bring to a boil. Reduce heat; cover and simmer until crisp-tender, 7-9 minutes. Drain, reserving ¼ cup cooking liquid. Transfer carrots to a 1-½-qt. baking dish.
In a small bowl, combine the mayonnaise, onion, horseradish and reserved cooking liquid; spread evenly over carrots. Sprinkle with cheese; top with cracker crumbs. Bake, uncovered, for 30 minutes.
