Chop cabbage and beets in a food processor until finely shredded.

Combine the chopped cabbage and beets in a large bowl.

Add the sugar, salt, black pepper, and red pepper to the mixture.

Incorporate the grated horseradish into the bowl.

Thoroughly mix all ingredients to ensure even distribution.

Pack the mixture into quart jars, filling them slightly over 3/4 full.

Cover the mixture in each jar with cold white vinegar until fully submerged.

Seal the jars with lids.

Refrigerate the sealed jars.

Let the relish sit in the refrigerator for at least a day before consuming.

Optional: For canning, bring the relish mixture to a boil.

Pack the hot mixture into hot, sterilized jars.

Cover the relish with hot vinegar.

Seal the jars and allow them to cool, ensuring the lids seal properly.