Praise be to Allah.
There is nothing wrong with using the desert air cooler during the day in Ramadan, and inhaling the air that comes out of it is not regarded as breaking the fast, even if the air cooler is fed with water. Even if we assume that droplets of water come out of it sometimes, they dissipate in the air, so none of the water vapour droplets reaches the person’s mouth or nose, and nothing of that goes beyond his throat.
Inhaling air is permissible. The air that comes from the air cooler does not have any substance, like bakhoor (incense), for example, and the droplets of water with which it is fed do not have any substance in the air emitted by the cooler, especially if you keep away from it and you are not right next to where the air is emitted from the cooler.
If it so happens that a fasting person was close to the air cooler and is certain that some of the water droplets entered his mouth, he must spit it out.
For more information, please see the answers to questions no. 66079 and 289121 .
A person may feel less thirsty when there is an air cooler, just as he will feel less thirsty if he fasts in cold weather. That does not affect his fast, and it is not the result of water vapour in the air; rather it is because of the cold temperature that results from the air cooler, and the cool air that comes from other types of air conditioners is much colder than that which comes from these desert air coolers. Inhaling cold air does not have a greater impact than putting water on one’s body or head, because the moisture of water reduces the feeling of thirst. In fact, the skin absorbs water, but that does not break the fast.
Al-Bukhaari (may Allah have mercy on him) said: Chapter on bathing for one who is fasting. Ibn ‘Umar (may Allah be pleased with him) wetted a garment and put it on when he was fasting.
Ash-Sha‘bi entered the public bathhouse when he was fasting… al-Hasan said: There is nothing wrong with rinsing one’s mouth and cooling down for one who is fasting… Anas said: I have a tub in which I bathe when I am fasting.
Al-Haafiz Ibn Hajar said in Fath al-Baari (4/197): The [word translated here as] tub is a hollowed-out rock like a cistern. It seems that the tub was filled with water, and when Anas felt too hot he would sit in it to cool down. End quote.
It seems that this tub was like what is known nowadays as a bathtub.
Abu Bakr al-Athram narrated with his isnad that Ibn ‘Abbaas entered the bathhouse when he was fasting, along with some companions of his, during the month of Ramadan. End quote from al-Mughni (3/18).
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: What is the ruling on having a shower or bath more than once during the day in Ramadan, or sitting beside the air conditioner or air cooler all the time, when this cooler emits moisture?
He replied: In the previous answer, we spoke of evidence which indicates that that is permissible, and there is nothing wrong with it. The Messenger (blessings and peace of Allah be upon him) used to pour water over his head because of the heat, or because of thirst when he was fasting, and Ibn ‘Umar (may Allah be pleased with him) would wet his garment with water when he was fasting, to cool himself when it was intensely hot, or because of thirst, moisture does not have any impact [on the fast], because it is not water that reaches the stomach." (Majmoo‘ Fataawa Ibn ‘Uthaymeen 19/285).
And Allah knows best.