Bring a large pot of water to a boil; add beets and cook until tender, about 30 minutes. Bring a separate pot of water to a boil; add potatoes and carrots and cook until tender, about 20 minutes. Drain vegetables, cool, and remove skins. Dice and place in a large bowl.
Place diced pickles in the bowl with beets, potatoes, and carrots. Drizzle olive oil and vinegar over mixture and toss to coat. Season with salt and sprinkle with green onions. Chill completely before serving.