The hot water has less dissolved gasses. In some cases it has less chlorine. I put water in a glass pitcher in the fridge because it tastes better after sitting at a lower pressure and off gassing. I agree that the water enters the ice maker at room temperature, but it may not be a bad idea regardless.
If it's heated within a closed system (i.e. mains pressure hot water), the gases are still there - they can only leave the water if you have an open tank, which is a bit old-fashioned. You can observe this by running hot water into a glass from the faucet: it appears cloudy, which is the dissolved gases boiling off.
This means, once the hot water within the pipe has cooled (within the pipe) it'll still have the same gas content as cold water.
