Place eggs in a saucepan and cover with water. Bring to a boil; remove from heat and let eggs stand in hot water for 15 minutes. Remove eggs and cool under cold running water; peel eggs. Slice each egg in half lengthwise. Remove yolks and transfer to a medium bowl. Place egg whites on a serving platter.
Mash yolks with a fork. Stir in mayonnaise, horseradish, dill, dry mustard, salt, pepper, and paprika. Spoon equal amounts into egg whites.