Very good point. Actually now that I think about it after your post my wife has specifically commented on this as being something that concerns her - water up the nose if something happens with the mask (and why she is so quick to try to clear it when snorkeling if even a relatively small amount of water gets in).
I used to be in charge of getting people through the mask R&R drill for their OW when I was a DM candidate.
That's the toughest skill for the huge majority of people. Your nose and face is uncovered but you're supposed to breathe. It goes against every human animal instinct we have to try and breatbe when your face is submerged.
For the people that had the worst time with it I had a system. First I would take them to the shallow end where we could work on it away from everyone.
I would start by having them flood their mask just partially and just breathe. Then have them flood it a little more (not covering the eyes yet) and breathe. I had a slate that said "You're breathing air with your nose underwater right now, no big deal right?". To which they agreed.
I also made it clear before we started that they could just stand up and be out of it if they absolutely had to.
Next step was to flood the mask completely even if it took a few more partial floodings to get there. Once their mask was totally flooded I had them just continue to breathe.
At that point I would pull my mask away fully flooded and let it settle back in place fully flooded.
I was doing the whole drill with them so they could follow my lead. after a time or two of that we would remove the mask and just breathe. They realized that there was no difference breathing with the mask off than a partially flooded mask. Your nose is useless underwater. I would get them to relax, which they were already because of so much gradual work towards getting the mask fully off. If they freaked out and couldn't take it any more I'd have them shut their eyes and concentrate. A lot of times this would work. If not then I'd have them shut their eyes and hold their nose until they calmed down, then they could slowly let their nose go and slowly open their eyes.
Once they acclimated and got the hang of it they did fine. It's a total mental game and gaining power to overcome instinct, that's all it is.
When you're diving normal wearing your mask there is always going to be a few drops or maybe a teaspoon or tablespoon of water in the nose pocket, enough that if your were to suck it up into your nose it would be very uncomfortable. But we breathe and don't think about it because we can see and the rest if our face is dry. But really there is no difference. It's all mental.