When water coolers first became popular many years ago, they only dispensed cold water, so that were called water coolers. Nowadays they can also dispense hot water, but the old name stuck. You could call it a water dispenser if you prefer. If you were to name it for it's heating ability, you'd have to call it a water heater, not a water hotter, but that name is already used for the appliance in your house that heats the water for your sink and bath.

I am a American and in my state, a water cooler is a box used to make your drinks colder. It is a box that you put ice into to cool your drinks. So when someone asks you " can you get me a drink from the water cooler" they are asking for a COLD drink. Water hotter is not a word. We never use it. Hope this helps :)