Place eggs in a large saucepan and fill with cool water. Cover pan and bring to a boil over medium-high heat. Remove pan from heat and let sit for 15 minutes. Drain hot water, leaving eggs in pan. Fill pan with cold water and a cupful of ice. Let eggs cool completely.
Meanwhile, whisk together yogurt, mayonnaise, mustard, vinegar and horseradish, pickle, salt and pepper. Set aside.
Peel eggs but keep them intact. Slice in half lengthwise, scoop out yolks and mash. Set aside egg whites.
Add mashed yolks to yogurt mixture; stir to thoroughly combine. Transfer mixture to a pastry bag or a zip-top bag with the corner cut off. Fill centre of egg white halves.
Garnish tops with sprinkle of smoked paprika and chopped chives.