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What do we know about extraterrestrial snow? On which (exo)planets or (exo)moons do we have direct hints for its existance? This is indeed a children's question, but I struggle to answer it conclusively.

I only know about snow on Mars, Venus snow (which strictly speaking might be a misnomer) and snow on Titan.

For exoplanets in the habitable zone, the phase diagram of water may of course allow snow if water existed on an exoplanet. What about non-water snow? Which chemical substances which allow snow have been observed so far on other (exo)planets?

Generalized definition of snow

As snow I would define as precipitation of any (chemical) kind which is not in liquid or gaseous state. The solid objects (most likely crystals) should be moving downward in from the sky and is possibly reaching the ground (if there is any).

This definition excludes ground frost and hail. Hail is excluded since these layered balls of (water ice and/or other solids) are actually moving repeatedly and significantly moving upward (on Earth in Comulonimbus clouds). The definition does include solid clear sky precipitation aka diamond dust.

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Four locations in which "snow" might be falling.

The most Earth-like moon might be Titan. It is large enough to have a substantial atmosphere and there seems to be an "ethane cycle" that mimics the water cycle on Earth. It is likely that there is ethane snow near the polar regions of Titan. This is mentioned on the Wikipedia page on the climate of Titan

Io is not Earth-like at all, but it does have so many volcanos that spew hot sulphur vapour into the sky. This sulphur sublime to sulphur crystals that fall to the ground as "snow". However, with no atmosphere to speak of, the crystals will be falling ballistically, and even though surface gravity is weak, the'll be moving pretty fast when they reach the ground. See this article in Nasa science

There are cirrus clouds in the atmosphere of Neptune. And just as if you were to go into a cirrus cloud on Earth, you would find that they were full of crystals (of ice on Earth, but Methane on Neptune). And like on Earth, they would be falling down. On Earth, the ice in cirrus clouds turns back into water vapour long before it reaches the surface (so these don't fit your criteria). On Neptune, there is no surface, so the "reach the surface" aspect is moot. You might call these "snow", if you were in a hot air ballon and floating along with them.

There is speculation about carbon precipitation in the form of diamond in the lower atmospheres of some of the giant planets - leading to romantic headlines about "snowing diamonds on Jupiter."

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It most certainly snows on Mars. As described on this Earth Science SE answer, evidence exists for both water and carbon dioxide snowfall on that planet, with carbon dioxide presumably more prominent given the composition of the Martian atmosphere.

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