Nearly all clouds are made of either fog or ice-dust. Fog is tiny, tiny bits of liquid water. Ice dust particles also start tiny but they can grow into snowflakes if water-vapor is added to the cloud.

Rarely, clouds can contain other things like dust from a sandy desert or ash and acid from a volcanic eruption.

Fog is possible at temperatures below freezing. It's not completely stable - it wants to freeze - but it doesn't freeze immediately. Things like the age of a cloud, its temperature, and the amount and kind of dust in the air predict whether freezing starts.

Below freezing temperatures, ice dust is more stable. So once a cloud starts to freeze, the growing ice crystals "steal" the water from water droplets, even if they never touch.

Cirrus clouds and contrails are made of ice dust. They form at very high altitudes and cold temperatures.

If you see snow, you can be sure that it came from an icy cloud. Rain usually comes from wet clouds, but icy clouds can make rain if there is enough warm air below them, so this depends on the season.

Thunderstorms seem to always have ice at the top, and they usually have wet bases.

Modern radar systems can see a difference between wet fog and ice dust and especially snow. This is mostly useful for research, but it's also interesting for aviation. Freezing wet fog will stick to solid objects and form ice - this is especially dangerous for small aircraft. Ice dust and snow don't do that.