Preheat the oven to 425°. On a baking sheet, toss the squash with 2 tablespoons of the olive oil; season with salt and pepper. Roast for 20 minutes, until tender. Spread the hazelnuts in a pie plate and toast for 6 minutes, until golden. Let cool, then chop.
In a large bowl, toss the arugula, frisée, prosciutto, chives, hazelnuts and squash. In a small microwave-safe bowl, mix the remaining 1 tablespoon of olive oil with the vinegar and hazelnut oil and season with salt and pepper. Microwave the dressing until hot, about 1 minute. Pour the dressing over the salad, toss well and serve.