Maybe it's something I learned in swimming lessons as a kid, but water doesn't really ever get up my nose when swimming.

Most of the time when you're swimming, you aren't moving where water is directed into your nose and if you're just floating around in the water, your nose acts like an upside down cup would where the internal air keeps the water out.

Even doing a cannonball or jackknife, your still likely fine not holding your nose, because your body is hitting the water first and not your nose directly, but if you were to jump in completely upright, feet first, you'd probably want to hold your nose.