Heat oven to 400°.
Toss carrots, parsnip, garlic, and onion with 2 tablespoons oil and season with salt and pepper. Spread on a parchment-lined baking sheet. Toss beets with remaining 2 tablespoons oil and spread on separate parchment-lined baking sheet (to prevent bleeding). Roast both sheets of vegetables until tender when pierced with a knife, tossing midway, 30–40 minutes.
Allow vegetables to cool slightly, then toss with fresh arugula. Dress salad with Maple-Apple Cider Vinaigrette (recipe follows) to taste, and garnish with toasted walnuts and crumbled goat cheese.
Whisk all ingredients together until combined and creamy.