I have had peeled whole horseradish root submerged in 8% vinegar stored in the refrigerator for six months. Has it been there too long?

in theory, as the French say, some food-safety or duration sites advise 4 months max.
in practice, as they also say, I've used prepared horseradish (similar to yours, in vinegar, but grated instead of whole) between 6-12 months and found nothing wrong with it except a little dulling of the nuclear-strength hit you get from freshly made or freshly opened.
I would open the jar, check the horseradish for signs of mould or other degradation and - if no such signs - taste and use.