The cloudiness should go away. It is probably very fine bubbles suspended in your water. Maybe there is something goofy with the way the hot water enters the aeration attachment on the end of your faucet...most faucets have these unless it is a utility-type faucet located in a laundry room. If your hot water tank is old, it could be a problem with the hot water tank itself.
Anyway....get a large glass of warm cloudy water and let it sit to see if it clears up. If it doesn't, I would be worried about water quality from your hot water heater!
Adding ice cold water as part of a water change is not a good thing...even for goldfish.