Cook beets in boiling water until tender, about 20 minutes. Drain beets, remove skins and chop finely. There should be about 2 cups. Mix beets with onions and peppers.
Combine vinegar, sugar, salt, and horseradish in a large stainless steel or enamel saucepan. Bring to a boil over high heat. Add vegetables. Return to a boil, reduce heat and simmer, uncovered, for 20 minutes, stirring occasionally.
Fill hot, sterilized jars to 1/2 inch headspace. Remove air bubbles, adjust headspace. Wipe rims with a towel dipped in hot water, place hot lids on jars, add ring adjusting to finger tightness. Process in a boiling water bath 15 minutes for half pints and 20 minutes for pints.
Makes 3 1/2 cups.
NOTES: The recipe says you can use a 14 oz can of beets in place of the fresh ones. Also, you can use commercially prepared horseradish in pace of the fresh, just double the amount.