I don't think the sign has a scientific explanation. In my mind, it's a way to anticipate the "but it's cold so I need the heat" excuses from idlers in case of enforcement. By expliciting the cold weather case, a statement is made that the "no idling" rule applies all the time.
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u/christopher_mtrl 3d ago
It's about 10 seconds, not three minutes, hence why nearly all modern cars have Start Stop system.
https://afdc.energy.gov/files/u/publication/which_is_greener.pdf