Possibly. I would suggest this is because either, rings and jewelry are more likely to trap liquid nitrogen against the skin for longer in the event of a spill. And second, because the jewelry is likely to stay cold for longer thus increasing the amount of time the cold is in contact with your skin. Usually small drops of liquid nitrogen on the skin will evaporate away so quickly as to do minimal damage. Larger amounts of liquid nitrogen would be more of a problem.
Now having said this, it is usaul practice to wear protective gloves clothes shoes and face shield when handly liquid nitrogen so that the liquid never actually contacts your skin in the first place.
I the case of a fictional story I would say that pouring liquid nitrogen over a limb wearing jewelry could quite possibly make the skin freeze to the metal... ouch!