1. Whisk pomegranate juice and vinegars in bowl. Gradually whisk in oil. Season with salt and pepper. Rewhisk before using.
2. Melt 2 teaspoons butter in heavy large nonstick skillet over medium-high heat. Add 1/3 of squash wedges. Cook until browned on both sides, about 5 minutes total. Transfer squash wedges to rimmed baking sheet. Repeat 2 more times with remaining butter and squash wedges. Sprinkle squash with salt and pepper. (Can be prepared 6 hours ahead. Let stand at room temperature.)
3. Preheat oven to 450°F. Transfer squash to oven; bake 20 minutes.
4. Mix greens, pomegranate seeds, and pine nuts in large bowl. Toss with half of dressing. Divide among plates; top with squash. Drizzle with dressing.