When the potatoes are cold through and through, remove the plastic wrap and add the crumbled bacon (reserving 2 tablespoons for garnish), chopped hard-boiled eggs (if using), mayonnaise, 1 tablespoon of the horseradish, and thinly sliced green parts of the green onions (reserving 2 tablespoons for garnish). Gently toss to combine, taste the salad, adjust with salt, pepper, and additional horseradish (if needed), stir again to combine, and adjust as necessary. Cover tightly with plastic wrap or transfer to an airtight container, and refrigerate for at least 2 hours, but preferably overnight before serving. Before serving, stir well, taste, and adjust with additional dressing if needed. Garnish with reserved bacon and green onions!