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It sounds like you have a horseradish plant so I hope your plant is big enough to start getting what is the end result. Even if you do not and are interested in when it gets harvested, here is what the experts agree upon. You can harvest in the fall, right after the first frost. You can also harvest in spring.
Dig as deep as you can go and pull the root from the ground. You can also break off some of the roots and replant if you would like.
Ground what root you pulled out and not replant into horseradish.
Some like spring better as that is when the root is hottest. Spring is when you should plant for the next year harvest and although anytime of the year is fine to harvest, spring seems to be when it is hottest. That is if you want the horseradish to be hot!
Hope this answered your question. Please let me know if I can answer anything else on this topic and please rate my answer so that I can get an understanding if my answer was helpful.