Asthma is not a curable disease (like most other medical conditions), but can be controlled perfectly. It may be genetic , though the inheritance pattern is still not clear. Even an individual harbouring the 'trait' may not express symptoms in his lifetime depending on circumstances. So even if the family members whom you have seen, have not obviously suffered from the disease, does not mean that they have not been carrying the gene! Even if you do not smoke, you should ensure that you do not get exposed to passive smoking. Undue exposure to exercise in cold may precipitate am attack as a 'trigger factor' if you are asthmatic.