Put the potatoes in a large pot and add water to cover; season with salt. Bring to a boil, then reduce the heat and simmer until just tender, 10 to 12 minutes. Drain and transfer the potatoes to a large bowl. Add the vinegar and 1 teaspoon salt and toss. Let cool.
Bring a saucepan of salted water to a boil. Add the snap peas and cook until crisp-tender, 1 minute. Transfer to a bowl of ice water, then drain and halve lengthwise.
Whisk the mayonnaise, sour cream, horseradish, mustard, 2 tablespoons water and the lemon zest in a bowl; season with salt and pepper. Gently stir into the potatoes along with the snap peas, celery, dill, chives and parsley.