Something that's falling is dropping or plummeting. Falling snow is drifting down from the sky to the ground.
If you see a sign that says, "Caution: Falling Ice!" it means you should watch out, because ice is breaking off the building above and dropping to the sidewalk below. On the other hand, if you are preparing for falling temperatures, you're getting ready for the number on the thermometer to decrease, or go down. Falling prices at your favorite store are like this too, getting lower or going down.