In a pot of salted boiling water, cook the green beans for 4 to 5 minutes or until tender. Drain and plunge into ice water. Drain well.
On a work surface, split the beans lengthwise, if desired (see note).
In a large bowl, combine the mayonnaise, mustard, vinegar, capers and horseradish. Add the beans. Season with salt and pepper and toss well. Transfer onto a large serving platter. Garnish with green onions.
Green beans split lengthwise makes them elegant, more supple and better able to absorb the dressing.