Bring a large pot of water to a boil; add beets and cook until tender, about 30 minutes. Drain beets; cool and remove skins. Dice and place in a large bowl.

Meanwhile, bring a separate pot of water to a boil; add potatoes and carrots and cook until tender, about 20 minutes. Drain potatoes and carrots; cool and remove skins. Dice and place vegetables in the same large bowl.

Add diced pickles to the bowl with vegetables. Drizzle in oil and vinegar; toss to coat. Season with salt; sprinkle with green onions. Chill completely before serving.