Fog does not really exist as a feature of minecraft, it is designed to help Minecraft run faster if you have the render distance turned down. To toggle fog and how thick the fog is go into the pause menu click options then video options. From here you can set the render distance, far has no fog while tiny has very thick fog. Please note that turning up your render distance may cause Minecraft to run slowly.
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Snow can go away in minecrafts, and can melt very slowly but it will still melt in the category its in on or by the minecraft.
use the hm-Defog (found in the great marsh-the "ace trainer" person has it)
If you have cheats turned on (which you do when you create your world), open the chat box with t and type /weather clear
Dropped items will eventually despawn. The amount of time it takes differs, they go away more quickly if you move further away from them.
You cant go to Olympus but you can go to the nether.