Place beans in a large pan and cover with 1 – 2 inches of water reserving the flavoring packet. Bring to a boil, let boil for 10 minutes, remove from the heat and let sit for 1 hour. Drain the water from the beans, rinse and return to the pot. Add 8 cups water, the reserved flavor packet, and the carrots. Bring to a boil, reduce heat, cover and simmer for 1½ - 2 hours. Add the corned beef, pearl onions, cabbage, salt, pepper, mustard, and horseradish. Simmer for another 20 minutes or until the beans are tender. Adjust seasoning with more salt and pepper if needed.