Cough since it got colder, particularly at night. 22 year old, 44kg, can I still develop asthma at this age?

Yes. Although asthma was once thought to be a disease originating in childhood, this is no longer true. Virus infection is now considered a triggering event for the development of asthma. Occupational asthma is one example which clearly shows that adults can develop asthma from even a single exposure.