From the superpower wiki I heard that vapor is a medium for heat exchange, but when I did some research on it I found that heat exchange might need a closed system. In a fictional world how would a Water manipulator that can mess with vapor and ice change temperature to control air?
Possible on a Macro Scale
Manipulating the temperature to control the air currents is nothing to sneer at. It fact, the act of warm air hitting cold air is what causes many kinds of weather patterns. Now, assuming some, but not all, of the rules of thermodynamics come into play, you can introduce cold air. In order for a block of ice to become water, in must take in heat, and the usual way it does so is by taking that heat in from the air, thus becoming cold air. Similarly, the opposite - if you take liquid water and turn it into solid ice, that drains the heat from it.
So, the assumption here is that by manipulating the states of water, you can introduce heat and cold into the air. There would be some limitations, certainly. Weather operates on a very large scale, and is subject to the butterfly effect. Not to mention that you'd need to keep the object in their final state in order to achieve the heat effect. That is, you'd need a large amount of ice to defrost if you want to induce a cold front, and a large amount of ice to keep frozen after you induce a heat front. Large in this case meaning like 'large on the scale of manipulating small sea's worth of water', given that you are fighting the current weather system. Not to mention that the butterfly effect of weather could screw you over at any given point in time, but that's not really here or there.
Manipulating water to control wind on a micro scale is, sadly, not very useful. All you can do is cause hot or cold air, and on micro scales, all that does is cause air to rise relative to the air around it. Good for creating something like thermals if you want to launch a glider or something. Not good if you're looking to manipulate winds superhero-style to do pinpoint things like punch villains in the face a few dozen blocks away.
If you can manipulate (I assume that this means move by telekinesis) water, you can just form drops (the smaller the more heat exchange you will get), and force these to expand, and by this lower the pressure in the drop. the drop will evaporate on the surface (here you "manipulator" probably causes a funny thermodynamics!), extract thermal energy from the environment (and freeze in the end when heat exchange with the environment breaks down if that happens before it's evaporated).