Why doesn't dry ice placed in water freeze the water?

There are a couple of effects here. One is the Leidenfrost effect: the dry ice is vaporizing very rapidly, which creates a layer of vapor between the dry ice and water. That vapor transfers heat very poorly, which keeps any particular drop of water from staying in contact with the ice. read more

There's little heat transfer to the water, so the vapor is really cold, and the water doesn't lose that much heat. Of course, the heat to vaporize the dry ice has to come from somewhere, so it is sucking some heat out of the ice. read more

If you put a bit of water in a bowl made from dry ice it will freeze. Dry ice is tricky though in a couple of ways. It sublimates in earth atmosphere, meaning it goes from solid to gas without a liquid phase in between. This makes the warmer water"dance" on the sublimating dry ice, which is giving off gas due to absorption of heat from the water. read more

Therefore, for ice to freeze the surrounding water, the ice must be cold enough that it can afford to gain enough energy to invoke this state change, without melting itself. Now, solid ice has a lower volumetric heat capacity; it only takes about 1.9 J/(mL*K) to change its temperature. read more