Place the eggs in a saucepan and cover with cold water. Bring to a boil, then remove from heat, cover, and let sit for 12 minutes.
Drain the eggs and transfer them to a bowl of ice water. Cool for 5 minutes, then peel under running water.
Slice each egg in half lengthwise. Remove the yolks and place them in a mixing bowl.
Mash the yolks with a fork. Add the mayonnaise, mustard, salt, pepper, and green food coloring. Stir until smooth and evenly colored.
Spoon or pipe the yolk mixture back into the egg white halves.
Arrange the filled eggs on a serving platter. Sprinkle smoked paprika lightly over the tops.
Place the dry ice in a small heat-safe bowl or cup set in the center of the platter. Add a few drops of warm water to create fog just before guests arrive.