Preheat the oven to 375°. In a baking dish, lightly drizzle the beets and thyme with olive oil. Season with salt and pepper. Cover with foil and roast until the beets are tender, about 1 hour and 45 minutes. Let cool, then peel the beets and cut them into 3/4-inch dice.
In a large bowl, whisk the vinegar with the mustard. Whisk in the remaining 1/2 cup of oil until emulsified. Add the horseradish and season with salt and pepper; toss with the beets and pistachios. Transfer the beets to a platter, top with the apple and serve.