Your nose is full of tiny little blood vessels called capillaries, which supply oxygen to your nose itself. These capillaries need to be close to the internal surface of your nose (its mucosa) in order for the tissue to stay alive. Because they are so tiny, capillaries are friable, meaning they can break under relatively minimal pressure, such as from repetitively blowing your nose. If you are on blood-thinning medication, such as Coumadin or Plavix, it is recommended that you do not blow your nose, because you are at risk of having a dangerous nosebleed that is difficult to stop while taking these medicines. This situation is made worse when it is cold and dry, making the mucosa of your nose even more susceptible to damage. This is quite similar to a kitchen sponge, which is much easier to break in half when it is dry. Your second question is largely a personal one, as each person's body is different. Using less force when you blow your nose will probably reduce the incidence of the nosebleeds, while ceasing to blow your nose will stop them altogether. Assuming that you do not have a bleeding
condition and are not on any medicines that would make a nosebleed very dangerous, it is ultimately up to you to balance the risks of nosebleeds against the benefits of nose blowing.