We have a bed or Common horseradish here in the western U.S. that's been there for over 15 years. It does tend to spread, but not invasively so. Ours went froma small cutting to a patch about 4 feet square in that time.
The leaves make a great salad during the summer, but don't harvest the roots for canning until after the frost kills the leaves back.
On harvesting, I take the roots to the garage after thorough washing, peel them and grind in a food processor. You'll want plenty of ventilation! Pack them in 1/2 pint jelly jars, mixing about 1/8 cup (maybe and ounce) of apple cider vinegar per jar, and perhaps 1/4 to 1/2 teaspoonfull of good Kosher or Canning salt (don't use table salt, it's iodized). Place them in the back of the refrigerator and don't disturb for at least 2 weeks, a month is better. Use only a little bit until you determine the strength of your mixture... Bon appetit!