Thank you for your question to Ask the Expert.

Here is a great publication on growing horseradish: http://www.extension.umn.edu/yardandgarden/ygbriefs/h209horseradish.html

Yes, this plant will over winter so you can leave it in the ground for the winter, but will need to set lateral pieces of root next spring in order to keep the plant producing high quality roots.  I would not remove the foliage yet as this plant is still putting on growth in the roots late in the season.  You might wait until the first hard frost to cut the folliage.

Please let me know if you have any further questions.

Weston