You can preserve harvested horseradish by drying or freezing. To dry, peel and slice the root into uniformly thick pieces. This can be done using a food processor or knife. Spread the horseradish in a single layer on parchment paper placed on a cookie sheet.
Set the oven to the lowest temperature, or use just the heat of the pilot light if the oven is gas. Turn the horseradish pieces, and check them for dryness while in the oven. The pieces should be brittle to the touch. Remove them from the oven, and allow them to cool. Store them in a dark, tightly sealed container in a pantry or cabinet.
You can also preserve horseradish by freezing it. Wash and trim the roots, and place them in a freezer bag. Seal the ends of the bag tightly to form a vacuum seal. Store in the freezer until ready to use.