Pour the vinegar into a medium, non-reactive saucepan and stir in the sugar, salt, and black pepper. Bring to a boil and stir, making sure all the sugar is dissolved.
Meanwhile, mix the cabbage, beets, and horseradish together in a large glass bowl. Pour the vinegar mixture over top and mix thoroughly. Pack into sterilized jars and seal with vinegar-proof (non-reactive) caps. Store jars