Peel and wash the beets very well. Cut them into large chunks, put them in a pot, cover them with water, and cook until they are soft, about 1 hour.
Drain the beets, reserving 2–3 t. beet water. Puree the beets and mix them together with the horseradish root.
Add the remaining ingredients and let it sit covered in the refrigerator for 2–3 hours. Adjust the seasonings to taste.
For a sweeter taste, add more sugar; for a milder taste, add more beets; for a stronger taste, add more horseradish root. Add them each a little at a time as the smell can very quickly become overpowering. Refrigerate before serving.