Does drinking cold water on a hot day hurt your vocal cords/singing voice?

No its not true, not one little bit.

Nothing you eat or drink directly affects your vocal chords. (Of course.. a healthy diet contributes to the health of all areas of the body) There is a flap of cartilage at the base of the tongue, the epiglottis, this covers the trachea during swallowing to keep food or liquids from entering the airway/vocal chords. If this doesn't work.. you choke.

Considering that the vocal chords are along the main airway, it makes every sense that your body stops food going down.

Sooo.. In conclusion, nope cold water does nothing harmful to you vocal chords. although, some people find that it makes their throat cold/uncomfortable.

No, it does not hurt them because no food or water ever touches the vocal cords. They are protected and only open when you phonate, not when you drink. Some people say it's better to drink room temperature things while singing because cold drinks may shock your throat/make it cool down, but I don't think that's necessarily true. I think you're fine with what you're doing, as long as YOU don't feel like it's hurting your voice.

I like to drink hot water, a body good

No its defiantly not true