For every 3 points a horse accumulates it will age by 1 year. So, for example if a horse races in a claiming race (0.5 pts), a white race (1 pt), a green race (1 pt), and a blue tournament (1 pt) then it will have accumulated 3.5 points. So, it will age by 1 year and the remaining 0.5 pts will continue to carry forward. Notice that and entire blue or general tournament counts as 1 pt. A horse will most likely race in more than one race in a blue or general tournament but will only age by 1 pt for the whole tournament and not each race in the tournament.
So, if a horse is not racing it will not age. It only ages if it is racing.