I read about this as a kid reading Freeman Dyson's "Imagined Worlds"[4]. Dyson's commentary is definitely worth reading. (Anything written by Freeman Dyson is worth reading.)
A cheese factory used ice ponds[5] for about 10 years, eventually abandoning them because the ice didn't last through the summer and it was difficult to maintain[6].
[1]: https://en.wikipedia.org/wiki/Ice_pond
[2]: https://www.washingtonpost.com/archive/opinions/1981/08/02/t...
[3]: https://en.wikipedia.org/wiki/Ted_Taylor_(physicist)
[4]: https://books.google.com/books?id=MOC8UJPuvO8C&pg=PA42
[5]: http://www.nytimes.com/1984/06/03/nyregion/dairy-hoards-500-...
Wouldn't you have to insulate your pond from below as well as above?
The storage facilities are called Ice House [0]. The large ones stored several thousand metric tons and could last through the whole summer, depending on the climate.