Dragonspear Castle Exterior is where you arrive from world map travel, it's shown as Dragonspear Castle on map, for obvious reasons.
In Chapter Ten – Allied Siege Camp, the crusaders camped here don't recognize your identity so you're free to explore and run quests until they do; in Chapter Eleven – Dragonspear Castle Battle, it will become a battle ground where you must push though enemy waves and venture into the Dragonspear Castle Keep First Floor.
The notes in the infobox are for Chapter Ten, except traps, which appear only in Chapter Eleven.