when I last looked ,back in the days when most cars had manual aircon (if any
) the conclusion was the extra fuel needed for the aircon was about the same as the extra fuel needed to overcome the extra drag when the windows are open.
You could save fuel if the ambient weather allowed you to tolerate the windows being shut without aircon. -
Except they also recommended, and probably still do, that you use air con regularly, even in winter (when it helps dehumidify) because lack of use can make refrigerant leaks more likely.
I think climate control means the aircon is self regulating. If cabin temperature remains close to your ideal setting setting anyway when the windows are closed it will only use air-con occasionally for short periods. Opening windows would increase fuel consumption in most circumstances plus the noise and unwelcome insects, etc.
With manual air con my wife preferred fresh air and birdsong , except if in a city centre, or at high motorways speeds. But she is much happier to have closed windows with climate control.