Why should you never break the ice on fishponds in cold weather?

Answer 1

Because you'll fall in. Duh.

Second answer from an editor:

The Fish get all the "oxygen" they need with the ice covering so you don't need to break the ice. The most serious reason you don't break the ice is that young children need to know the pond is icy. They are less likely to play on that ice if they see an entire sheet of ice and if they fall on it they may be saved by the thick ice. If the ice is thin then the children are at risk. It is a good idea to put up some type of barrier around any pond, water fountain or other artificial body of water (pools, etc) during the winter. If there are likely to be toddlers around them their should be a barrier year round. Children cannot tolerate being overly cold or have their lungs filled with water. Many who succumb to hypothermia or drowning can be save but they sadly are often left brain damaged or deaf.

One of the other reasons to leave the ice is the pond gets a new amount of fresh water and snow melt on it. The snow is rich in nitrogen and many other compounds that are beneficial to the fish. Did you know more fish lay eggs and successfully have their eggs become fish that survive? This is because the ice protects the new fish from predators. The lakes have an increase in the fish during the winter so that by summer there is a new crop of fish for the fisherman.