Why does beating egg whites with cold water increase the volume of incorporated air
When you beat an egg white, you incorporate air into the water contained in the egg white, thus making an emulsion. The kind of foam that we obtain is the result of the proteins present in the egg white trapping the air in the water.
So it makes sense that if you add a little bit of water you will produce more foam. I assume it has to be cold water because emulsions are fragile and would be destroyed by hot water.
Careful with the quantities though, I haven't been able to find a clear table of quantities but most of the recipes mention just one coffee spoon of cold water.