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Up to a point. It's not that the air needs to be cold, it's that it needs to be cooler near the ground than above it. Sound travels faster in the hotter air, and sound waves curve and refract from the zone of higher speed into the zone of lower speed.

So in the night, when the air gets colder, the sound from up above tends to curve towards the ground and propagate farther. During the day is the other way round. More to read: https://blog.thermaxxjackets.com/refraction-of-sound-waves-acoustic-shadows-explained

I hope this gets more scientific discussion, but I'm very sure this effect happens. When I lived in MN if I'd go outside on the absolute coldest days, like -30F sort of days, the one thing that always struck me was how loud everything seemed, from the crunching of snow under my feet, or even neighbors at the end of the block talking in a normal speaking voice and yet still being able to hear what they were saying.

Edit: Did some Googling, and apparently the explanation about refraction is correct? Essentially the ground air is extremely cold but there's a layer of warmer air above which effectively ends up bouncing the sound waves back towards the ground allowing them to carry much farther than normal

If it snows, snow is a pretty effective sound absorber and can make sounds sound clearer due to the lack of reflections on surfaces covered in snow. It wouldn’t be louder though, it would be softer.

If you mean without snow, I have no clue.

I would imagine yes but that’s because humid air is less dense. The more dense the air the faster waves can travel, so dry may equal farther distance sound can be heard.

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Would be the opposite, no? Sounds travel faster and further underwater than in air.
Would be logic that high humidity air allows sounds to travel further too, no?

Tempeture gradients can conduct sound along the ground. Importantly, snow being a good sound absorber tents to quiet everything down.

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