A general answer to this question is this:
The cold water will condense more water than hot water. Condensation is when something that is a gas, changes into a liquid, usually by being cooled down.

But here is more background:
Lets start with some important stuff: There are generally three types of matter: Solid, liquid, and gas. Solids are like sugar, salt, or ice, liquids are like water you find in lakes and the ocean, and gasses are like the air you breath. The air, however, is made up of lots of different types of things. This includes oxygen (which we need to live), nitrogen and many, many, many other gasses. One of those gases is water gas.

For your question we will talk about the condensation of water gas into liquid water.

So, how is water floating around as a gas in the first place? Think about when your parents are cooking, or when they make tea or hot chocolate. They might boil water, right? When the water gets really hot and boils, it starts to bubble. What are the bubbles? The bubbles are actually water gas!

When you boil the water, you have added enough energy into the water to make it stop being a liquid, and make it float away. That is why if you heat water long enough you can make it all disappear...it all escaped as gas! The water has EVAPORATED. Water is evaporating all around us all the time - constantly from the ocean, constantly from rivers, and constantly from plants and trees - you should look up what is called The Water Cycle to see how rain clouds form and water is recycled on Earth.

But now this: How do you turn water gas to liquid water? Well, you would do the opposite of heating it up. You would need to cool it down!

So, this is why a glass of ice water starts to have water form on the outside of the glass. The cold glass is cooling the air around it so much, that the water gas floating around in the air is becoming so cold that it can turn into liquid water on the outside of the glass - or condensing on the glass.

It doesn't have to be a cold glass of water though, it can be anything cold! You could try this experiment - put a metal spoon in the freezer and also put a metal spoon in the fridge for ten minutes, then take them out and leave them on a counter. What happens after 2 minutes? 5 minutes? Is there a difference in what happens to the spoons? Why do you think?

There are two ways I see to take this, and I will try to address both of them.

Condensation occurs when there is more water in the air than the air can hold. However, the amount of water the air can hold depends on the temperature of the air, with warm air being able to hold more water. This means the point of too much water can be reached either by reducing the temperature of the air, or by increasing the amount of water being evaporated.

If the water in your question is in a glass on a table, then air that touches a glass of cold water will decrease in temperature by more than air that touches a glass of hot water, and more condensation will form on the outside of the glass of cold water. On the other hand, if you have a large amount of water and some cold surfaces nearby, the hot water will cause more condensation on the cold surfaces because there will be more evaporation from the hot water than from the cold water, and therefore there will be more water in the air.

Both of these can be checked easily. Fill one glass with ice water and another with hot water, and leave them somewhere. If the humidity is high enough on that day, then droplets of water should form on the outside of the glass of cold water and not on the glass of hot water. You may also have noticed that the bathroom mirror fogs up after a hot shower, but doesn't after running cold water. This is because the hot water increases the humidity in the room, but the mirror is cold and causes very small droplets to condense on it.

In order for condensation on a surface of a container to happen, the temperature of the water inside must be below the dew point of air. On an average day in Santa Barbara, the dew point is 67°F. As long as the water temperature is lower than 67°F, droplets should appear at relatively the same amount for any water temperature. Of course, if you make “cold” water by putting it in the fridge (35°F) and make “hot” water by boiling it (212°F), then the cold water will condense water vapor but the hot water will not condense any at all.

Hot water evaporates more rapidly because the motion of the water molecules (what heat is) is fast enough to break them apart from the forces that hold them together. In a dry environment, however, any water, at any temperature, will eventually evaporate, because the air itself is starved for water and there is energy to be released by the water turning into vapor.