Most ponds deeper than 3 feet are less likely to freeze completely, however, this has a lot to do with your location and particular conditions. The rate in which ice grows depends on the ambient temperature, the wind, snow cover, and how thick the ice is currently. Thick ice grows more slowly than thin layers of ice, and a cover of snow delays the process further. Most fish require about 2 or 3 feet of water to move around in, even in their winter dormancy. Make sure your pond depth takes into account how much ice you expect to see, and leaves 2 or 3 feet underneath for your fish to live.
In most parts of the country, as long as your pond is deeper than 6 inches, it is very unlikely that it will completely freeze.