Judging by some of the comments on here, anyone would think that British roads were absolutely crawling with fellow cyclist and pedestrians.
Common sense should prevail. If you choose to spit or 'snot it', or not, should be up to the individual. I spit and clear my nostrils when necessary and always away from other traffic/people. I direct my aim to the kerb, making sure a ped. isn't approaching, and always look behind prior to doing so.
I've suffered with sinusitis for most of my life and have got used to the need to clear mouth/nose when necessary. I do not spit/snot in pedestrian or built-up areas when I'm on foot, as I will use my handkerchief which I always have with me.
On a bike, though, I don't bother, for the reasons mentioned above.