I sounds a little like the ice-house Dick Cavett lived in ("Strange, Dear, but True, Dear" - 9/11/09 - NY Times) that had been converted into a dwelling. "Ice-house" hereabouts in NY have different types, some subterranean, like the the William Floyd Manor, part of the Fire Island National Seashore) which has a circular stone wall, capped by a conical wooden roof, deep enough for a ladder, another small square pit at the Captain Brewster Hawkins House, East Setauket, NY (in the Town of Brookhaven Historic District) to the wooden double walled, straw filled above ground small "barns" built on Staten Island in NYC. Perhaps why it was located in the bottom of the drainage to control seepage? The Waverly Mansion, near Columbus, Mississippi was known to have had ice delivered from Boston, MA (William H. Adams) and stored somehow there, with its own natural gas generator, perhaps still awaiting discovery underground? It certainly sounds it would carry the load of ice and the slate slabs perhaps for load and insulation?

Speaking of ice, I recall the "Los Vicos" project in Peru, where Cornell University bought, ran and studied a Peruvian "plantation" the story was the natives had to go up into the Andes to the glacier to bring ice back for the landowners. The large plantations were  later broken up in "The Day of the Condor" land redistribution day. in the agrarian reform there.