I have a theory.
My theory is that the Disc, the elephants, and the turtle, are all surrounded by air, thus allowing everything to breathe. This would also allow the water that falls off the Disc to remain gaseous/misty, since it would be warmed by the daily passage of the sun.
Below are how I envision the orbits of the Disc's sun and moon:
orbits are possible orbits I imagined the sun taking. I've put these further out because the sun burns the outside of the moon black.
orbits are possible orbits that I imagined for the moon. I seem to remember reading that the elephants have to occationally cock a leg to let the moon go by.
Note: I think it makes more sense if both the sun & the moon orbit the Disc AND the turtle, but that the moon, or both the moon and sun, rotate around the Disc as they orbit it, so that once or twice a month the sun & moon are lined up, so the sun can burn the back of the moon, and as the moon moves around the Disc, it would appear to be waxing & waning.
, my theory is that the orbiting sun keeps the cold-blooded turtle warm, and the water that falls off the Disc gaseous. Then, the gravitational fields of the sun & moon, along with the action of the turtle's flippers, circulate the water vapor around the Disc, where it cools down and condenses into rain and snow.