House idea: Improve A/C efficiency with cold water

Can the cold water coming into your house be used to make your air conditioning system more efficient?

Consider a system like the following:
When the cold water comes into the house it goes into a tank (like a water heater) and the A/C system heats up that water to a set temperature (only to the point where it was still cool). So instead of having cold water at the tap you would only have cool water.

Notes:

• The A/C system would have to work less because it is more efficient to pump the heat to the cold water than to the hot air outside.
• The hot water heater would work less because the cold water was already warmed some.
• Maybe there could be one hot water unit with 2 tanks -- one for the cool water and one for the hot water. The A/C system would warm both(to different temperatures) and there would be a normal heater for the hot water when the A/C system didn't heat it enough. There could also be one tank for hot water and the cool water could be made by mixing some hot water with the cold water.
• Some of the cool water would still need to be cooled but probably very little of it (drinking water in the refrigerator, ice cubes, etc).

How much would this help? Is there a better way to use the free "coldness" of the cold water.