But it's not really inside. We need someone to post a photo maybe so you could see. I would call it more a covered hallway. It will generally be open on the ends to the outside, it just has a ceiling over it in some parts (which makes up the hallway floor of the level above you basically).
The hallways are NOT enclosed like you would see at deluxe resorts other than SSR and OKW. I would liken it more to a moderate hallway, except at the mods I've stayed in, all the walkways seemed to be on the perimeter of the building, whereas SSR has that + some interior-ish (LOL) hallways.
Speaking as someone who also has small children (OK, they once were small) and has stayed at SSR a number of times, there's nothing unsafe or unseemly about the setup at SSR.
As the hallways wind through the buildings, in some locations there are rooms on both sides so you're essentially in a standard hallway--two walls, ceiling, floor. In other sections there are doors on one side and a chest-high railing on the other with an open-air "window" above the rail. The opening is too high for it to present any danger to the children.
And the SSR setup is likely to minimize disturbances to fellow guests as you walk by. When staying in a traditional hotel-style building with interior corridors, most guests hear the families coming about 4 doors away since the sound (talking, laughing, crying, running, etc.) reverberates throughout the passageway. At SSR, the sound is allowed to escape and doesn't impact neighboring guests nearly as much.
This is the only "hallway" I've ever had at Saratoga. It's still open to the outside. I tried to find a view from "INSIDE" the outdoor hallway, but I couldn't find one.