Never an easy decision. For me, as an amateur, if this is a small concert that I was putting on for others for free and I know that people are travelling some distance in the bad weather and there are elderly people who will not manage the snow and I would feel responsible for their safety, then I would cancel.
If this were a paid concert, where I am only one of many performers, at a venue where they are responsible for the safety of the people arriving and leaving ... then i would feel that the show must go on. My own personal feeling. I am not the one with the lung infection.
If you cannot play because of your health, perhaps you can cancel your piece or get someone else to play it; i would ask my teacher for example.