I didn't play Skyward Sword, but I'm about half way through the 3DS Link Between Worlds game, and the handheld team is halfway towards this open world design already.
Right from the start, you can roam to most parts of the map (although you have to go around a wall of trees to an entry point instead of going being able to enter through the outer forest, I suppose) and there is a decent amount of side quests to take up between dungeons including fetch quests and collect-a-thons. You can just explore the area looking for secrets, too, and these are all things that I normally associate with open world games.