Obviously all of the modern things that we do to stay comfortable and do what we want to do is contributing to the problem of climate change because it pours pollutants into the atmosphere. And of course the universal use of air conditioning in civilized countries is a contributing factor.
Air conditioning is not helping the fight against global warming or global climate change in general, but, at the same time, there are other, bigger things that could be changed. There are so many people in the world that essentially restricting where they can live could lead to overcrowding, or forcing people to live uncomfortably because they can't afford not to.
While air conditioning units do make global warming worse, the theories related to global warming and cooling weren't created thanks to air conditioning. The fact of the matter is that tons of different issues gave rise to the theory of global warming and how humans are responsible for this issue.
This question made me think about parents telling them to close the door because they didn't want to pay to heat (or cool) the outside. Air conditioning is a tiny, minuscule sliver of types things that cause global warming. Global cooling at this point isn't a concern. Since air conditioning uses electricity, yes it is part of the problem, but definitely not the whole problem. Keep the door shut, cause I'm not trying to keep all of Atlanta cool, when it's a 105 out there.
No, I cannot clearly say that I believe that air conditioning is responsible for global cooling. There are most likely various causes of issues that our planet is facing today and will face in the future. It would be large generalization for me to assume that the only thing that is causing global cooling is air conditioning units.