The depth of the water isn't quite as important as the temperature. The fish obviously need enough water to cover their body. So long as the water doesn't freeze the fish metabolism will slow and the fish will endure. Unfrozen water about one foot minimum.
This will depend highly on your geographic location. However a pond that is over 6 feet deep should sufficiently hold them over through the winter. try adding a pond heater to keep the water ice free as well.
The water needs to be about 4 feet deep for koi to live in winter.They need plenty of swimming room if the water freezes over.If you live in a warmer climate then 3 feet would be enough.