Hex exit: It's mostly just to mimic how Dark Fort restricted movement with finite and specific door placements. In terms of narrative flavour, in keeping with the general Dark Fort/Mörk Borg vibe of impending and inexorable doom, it imposes the feeling of being lost in the woods (especially a malevolent and magical forest)--thinking that you're making progress and then stumbling across your own tracks from the day before. Definitely ignore that mechanic and explore in your desired direction(s) if that suits you better; since there's no destination there's no mechanical effect to moving in any direction.
Terrain types: totally just for flavour (aside from the keep/barrow). Would be cool to have it affect the monster abilities (i.e. bandits are stronger in the woods; wildmen are stronger in the swamp), but I'm not sure how to include that given the space constraints of the one-sheet rules format. I'm already bumping up against the edges just by using a D6 rather than D4 for encounters! I guess I could add the ballpoint-pen margin notes like in Dark Fort.