Put the eggs in a single layer in a saucepan, and cover with cold water by two inches. Bring the water to a boil, then remove from heat, cover, and let sit for 12 minutes. Remove eggs with a slotted spoon and cool under running water. Peel and cut in half the long way. Remove egg yolks and mash with mayonnaise, red horseradish, horseradish juice, white wine vinegar, Dijon mustard and salt and pepper to taste. Spoon or pipe back into egg whites and garnish with green onions. Serve immediately.