Tender, roasted beets and red onions pickled in rice-wine vinegar give this salad a distinctive flavor.
Heat oven to 350 degrees. Place the red beets in a roasting pan and the white beets in another roasting pan. Drizzle each pan of beets with 2 tablespoons olive oil; season with salt and pepper. Cover pans with foil; roast about 1 1/2 hours, until beets are just tender when poked with a fork. Remove from oven; set aside until cool enough to handle.
Meanwhile, combine the sliced red onions and vinegar in a small bowl, and let stand until the onions soften, about 30 minutes.
Gently rub off beet skins. Cut larger beets in half; transfer to a serving bowl. Using a slotted spoon, lift onions out of vinegar; arrange over beets. Whisk horseradish into vinegar remaining in bowl. Whisk in the remaining 1/4 cup olive oil.
Pour the vinaigrette over the beets and onions. Season to taste with salt and pepper; toss to combine, and serve.
Red and white beets vary slightly in their roasting times; check each one with a fork for tenderness.