I understand there's some alchemy going on here! Maybe some placebo effect also! :)

Your analysis is somewhat correct in that cooler air in denser. But a larger effect to consider is the reduced work-of-compression, which is proportional to input temperature in degrees absolute (Kelvin or Rankin). Any gas compressor is more efficient with a cooler input temperature. But you have to make a substantial difference in the temperature on the Rankin scale (deg F + 460). So I still think the effect of slightly better airflow is negligible. Now the difference between summer and winter is a different matter.

Gerald C