Sand

Aside from the fact that it piles up in dunes, the sand in Journey acts an awful lot like water. It's known to pour in sandfalls, flow through "aqueducts", and ripple from a player's chirp. That detail, with the fact that many cloth creatures resemble aquatic things, implies that Rythulia is buried under a literal "ocean" of sand.

Rolling in, and otherwise traveling through sand can often cover one's cloak in a layer of sand. Chirping can shake this sand off.

Snow
Mechanically speaking, Snow in Journey is basically white-colored sand.

In the beta
In the beta, sand would ripple in front of Wayfarers, and even "splash" in the Broken Bridge level. This made the analog to water even more obvious.

Dummied- out Murals suggest that much of the sand is from the bodies of the cloth creatures that were killed through the devices that Ancient Rythulians used.

Speculation
Companions turn to dust when the connection to the other player is lost. This supports the idea that the sand is from bodies of dead cloth creatures.

While a lot of the sand might have come from cloth animals, some of it might be from the bodies of ancient Rythulians, or as a punishment from the Mountain.

The combination of red and white dust might even explain how the Pink Desert got its color.