I don't believe it is the cold air that causes the heart attacks while people shovel snow. I suspect you would find their are other reasons for these deaths, such as people being unfit or people with existing heart problems (high blood pressure, artery clogging due to things like high cholesterol etc), - whether diagnosed of undiagnosed - suddenly doing rigorous exercise. If you suddenly turned off all lifts in any major city and people had to walk 4 or 5 flights of stairs to get to work you would also have a high mortality rate - and this is also not related to temperature.

As far as people not putting air conditioning on while they exercise, I put this down partly to the belief that sweating helps in weight loss, which is not entirely correct as you are only losing water which will be replenished anyway. The other side is that people at a gym are usually at different parts of their exercise. If I have been on a treadmill for 30 minutes, then I want the a/c on, but if I have just got to the gym it may be too cold if the a/c is already on. Some people also don't like cold air blowing on sweating skin, they may feel uncomfortable or are concerned it may lead to a cold.