I have an evaporative cooler mounted to my roof. The air comes straight down through a large vent in my living room. During winter, I wondered if cold air could come down through that large vent, but I could not feel any coming in (just put my hand next to the vent). I did not do anything to cover/seal the vent for the winter. Now that I am using the evaporative cooler again for the hot temps, I was reminded of this question.
Do evaporative coolers or the air ducts they use have a common mechanism for preventing air from flowing when they are off?