Hard boil the eggs; once they have cooled, slice them in half and place the yolks in a medium bowl.
Using a fork, smash the yolks until no lumps remain.
Add the mustard, mayonnaise, horseradish and sweet pickle relish.
Mix well, adjusting the ingredients to taste.
Add salt and pepper to taste.
Spoon the mixture into the eggs (or, for a fancier presentation, spoon the mixture into pastry bag and pipe into the eggs).
Garnish with paprika and/or olive slices. Serve immediately or chill for later.