Within the White Darkness is Chapter 13x of Fire Emblem: New Mystery of the Emblem. This chapter is reached if the player beats Chapter 13 in 20 turns or less on Normal (each higher difficulty progressively adds 4 more turns to this limit). Alternatively, the player can fill the requirements by preventing both enemy Thieves from escaping Chapter 13.
Chapter 13x is one of two chapters in New Mystery of the Emblem featuring Fog of War, which was absent in the main campaign of Fire Emblem: Shadow Dragon. The map is relatively small and has few enemies, including 4 Ballisticians. The boss, Clarisse, is a sniper situated towards the south east of the map and moves to attack any foes in range.
This map has a unique property in the sense that the enemies are hidden by darkened tiles of the map. This is to simulate limited vision people have in a blizzard. From the start of every turn, the visible tiles are within a mage's attack range of every unit on the battlefield. When a character is moved, that trail is dragged along but then covered up again in the next turn. If a unit walks into an enemy, the unit will stop in front of the enemy, and that unit's turn will end.
The Chest in the top-right corner of the map contains Iote's Shield, so be careful not to eliminate all the enemies until you nab it.
During the epilogue of this chapter, Clarisse limps back to the hideout injured, and is found by Reese. The story addresses the fact that Reese and Clarisse were raised in the same orphanage and Reese considers their bond that of siblings. When Eremiya finds that Clarisse is badly wounded, she asks Reese to dispose of her. Reese refuses, and soon after Clarisse asks Reese to stay with her as she dies, not wanting to be alone.