I couldn't get a clear picture to post of the outside of the cabin during the scene where Locke and Ben went to visit, but the second one I posted is of the one where Ilana and the group went to, obviously expecting to find Jacob there. It also had the ring of ash around it, so it's the same cabin, even though it's moved. The pitch of the roof is the same all of the times we've seen Jacob's cabin; it's different in Rose and Bernard's cabin.
It makes sense for Rose and Bernard to build a cabin during their three years on the Island. All they need is each other and for the Island to continue Rose's cure. And it makes sense for Jacob's cabin to be the one that Horace was building. After all, Locke found it by locating the blue prints and map after Dream Horace directed him to, so Jacob or Anti-Jacob directed him to the cabin through the dream. (One of them also influenced Locke to find the Beechcraft through a dream as well.)
The ring of ash seems to keep its occupant inside (whether it was Jacob or AJ), though it doesn't seem to keep the cabin from moving or appearing in another place (as it did with Hurley, though it's not clear whether this was the cabin physically moving or some sort of image projection). However, during Locke's second visit, he saw the ring of ash in the first location, though no cabin. He then found the cabin from Horace's map, so it was in a different location than when he first visited. We didn't see or hear anything about the circle of ash on this visit that I recall.