As for rinsing rather smooth surfaces, like your hands or dishes, I think the hot water works better. But the bubble-suppressing effect of cold water can be important to get detergent out of a sponge. I had a detergent that simply seemed to mulitiply if I tried to wash it out of the sponge with hot water.
As for hair I am not sure, it's somewhere in between, but i'm not going to try cold (nor very hot) water on my hair...