Cold water does not boil faster than hot water. Hot water occasionally freezes faster than cold water.
For those who don’t want to click on the link:
Cold water absorbs heat faster than hot water, but it has more heat to gain before reaching boiling point. And once it becomes hot, it will absorb heat at the same rate as any other body of hot water under the same conditions. In other words, boiling cold water involves both the process of making the cold water hot and the process of making the hot water boil. Thus it is not possible for it to take less time than boiling hot water, which only involves one of these processes.
Hot water will only freeze faster than cold water in very special conditions in which convection figures. Cold water will slowly lose heat and more or less freeze all at once, whereas hot water can be made to freeze in layers. Thus a portion of the hot water will freeze before any of the cold water. Hot water will sometimes freeze faster than warm water if the hot water is hot enough that it is losing mass while also losing energy (thus reducing the amount of water that needs to freeze). Note that this happens because mass is not kept constant.
If you want clearer and/or more technical answers than that, you’re going to have to click on the link.