How deep your pond should be will depend on how cold your location is, and how much ice you expect to grow on the surface of your water. 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.
You'll want to provide some way for gases to escape the water into the air and to allow oxygen to pass into the water. Use a de-icer or a heater to melt the ice in a section of your pond and provide access to the open air.
