Place potatoes, carrots and onion in 5 to 6 1/2-quart slow cooker. Top with corned beef brisket; sprinkle with contents of seasoning packet. Add apple juice and enough water to just cover brisket.
Cover; cook on low setting for 10 to 12 hours.
About 40 minutes before serving, remove beef from slow cooker; place on serving platter and cover to keep warm. Add cabbage wedges to vegetables and broth in slow cooker. Increase heat setting to high; cover and cook an additional 30 to 35 minutes or until cabbage is crisp-tender.
Meanwhile, in small bowl, combine all horseradish sauce ingredients; mix well.
To serve, cut corned beef across grain into thin slices. With slotted spoon, remove vegetables from slow cooker. Serve corned beef and vegetables with sauce.