Don't recall this one. As far as I remember, there are two outside grottoes at the Alfred Brehm House, across the pathway from each other and between is one of the entrances to the house. Even if old, they had grass, which would be visible even if this photo was taken in winter. So can you refresh my memory a bit.
If you walked towards the Alfred Brehmn House from the north and between the two grottos, this would be the one on your right, one distinguishing feature being the gap in the wall on the visitor side, which you can just see in the photo. I've never seen any grass in it (last visit in the spring of 2009).