Trim as much fat on the corned beef as you prefer and cut the corned beef in half to fit your slow cooker if needed.
Spray the slow cooker with non-stick spray if desired and put corned beef in the slow cooker with an onion that's cut into quarters.
Most corned beef comes with a seasoning package: you can use that plus additional garlic, whole cloves, bay leaves, whole peppercorns, and allspice berries. Use the spices you have or what you prefer. Add enough water to barely cover the meat.
Let the corned beef cook on low for about 5 hours, or until the meat is tender enough to pierce easily with a fork.
While the corned beef cooks, peel carrots and cut into diagonal pieces first, then smaller pieces. Cut a large head of green cabbage into quarters.
When the corned beef is fork-tender, add the carrots first and cook 20-30 minutes, depending on how firm you want the finished carrots.
Then add cabbage pieces and cook 20-30 minutes more.
For the horseradish sauce, whisk together sour cream, mayo, and cream-style horseradish.
Serve slow cooker corned beef hot with carrots and cabbage.