The arterioles ( smallest arteries in the arterial system) are very near the surface inside the nasal passages. They become more vulnerable to leakage during dry weather conditions.
Maintenance: Diminish the risk by maintaining the tissue by washing nasal passages using water that is warm or comfortably cool. Do this morning and evening. In between spray the areas with Xlear an over the counter item. Result- diminished need to sneeze which is a natural mechanism to free passages of undesirable airborne particles. In spite of the above, if you need to blow your nose, do so with small short moderate bursts of air.
Avoidance: In case of impending sneeze, open your mouth to diminish pressure through your nose. If one nostril is more likely to bleed as a result of sneezing, then partially close it with external finger pressure before sneezing. Alternatively, place your index finger horizontally- parallel with your upper lip, and press firmly against the area under your nose rearward and upwardly and maintain until tendency ends.
Treatment: If the above fails and a sneeze ensues resulting in nosebleed, gently pack the bleeding nostril with soft paper, the best is toilet paper. It's structural system is similar to clot formations by hemoglobin. Do not use any form of cotton. Leave in place for 5 minutes, then carefully and slowly rotate the paper plug while withdrawing slowly. If this is not successful, repeat and wait longer before attempting removal. If you've waited too long and plug resists removal, arrange the position of your head so that cool running water can travel outside your nose towards the tip. Result, the entire plug will become soaked and will likely be removable as above. Again, leave moisture inside nasal passages.
Cauterization of the offending area can easily be done by an ENT physician, however this should be a last resort. The treated nostril will be unpleasantly dry for a year or more because of the scar tissue that will form.