And for the record, as of a little over a week ago, there were only a dozen cases in Singapore according to the WHO. Even if they were mutually exclusive, Singapore isn't exactly the best example.
https://www.who.int/docs/default-source/coronaviruse/situati...
Air conditioning is actually very conducive to colds and the like. When you go from outside to inside you're usually sweaty and the air conditioning tends to make you too cold until you dry out. I've caught way more sniffles in the tropics than in the freezing climates.
On a tangent, I'd love to see a graph of illnesses during summer before / after the widespread adoption of AC.
https://www.the74million.org/article/exclusive-too-hot-to-le...
Even those that do have A/C don't cancel class when it breaks.
https://www.floridatoday.com/story/news/education/2019/09/11...
The real takeaway from the 74 Million piece is that information about HVAC in American schools is difficult to come by. It would certainly be interesting to look at COVID-19 in schools vis-a-vis A/C, but good luck prying information from the school districts about either infections or air conditioning. Perhaps it would be easier in a tropical country like SG where A/C is more of a necessity than a luxury.