For that matter, air conditioning could include humidifying or dehumidifying, but it doesn't: only cooling. Why weren't air conditioners called air coolers?
According to the Oxford English Dictionary, air conditioning has changed in meaning over time:
Originally: the process of cleaning air and controlling its temperature and humidity in connection with certain manufacturing processes.
Now usually: the process of controlling the humidity, ventilation, and air temperature in a building, vehicle, etc., esp. to maintain a comfortably cool atmosphere in warm conditions; (also) an installation or appliance which performs this process, an air conditioner.
The term was first used in the original sense in the early 1900s:
1909 S. W. Cramer Useful Information Cotton Manufacturers (ed. 2) IV. v. 1395, I finally hit upon the compound word, ‘Air Conditioning’‥. Suggested by the use of the term ‘Conditioning’ in the treatment of yarn and cloth.
1930 Engineering 11 July 34/2 Air-conditioning is dealt with fully, with the methods for washing, cleaning, humidifying, cooling and drying the air.
By the later part of the century, it was used solely to refer to cooling warmer air:
1987 C. Phillips European Tribe i. 11 Only the odd car rubbering by in the boulevard below and the hum of the air-conditioning disturbed my sleep.
So air conditioning was originally the cleansing of air, which already included temperature control. However, the meaning shifted over time to refer to any temperature control--but usually the cooling of warm air. It also shifted from industrial to more personal scope.
Probably the reason that air conditioning refers to "cooling" is because central heating was introduced first. Then the remaining problem to be solved became one of "too hot," rather than "too cold."
Also, air conditioners (and refrigerators) use a coolant called freon, that "conditions" the air. There are no similar chemicals that act on the air when it is heated.
I suspect that at the time they were introduced "conditioning" sounded like a comforting and effective thing to do - rather than merely cooling. In the same way that food mixers were called "food processors" when they were introduced because it sounded modern and technical.
A close ancestor to the modern air conditioner units was first made in 1902 by an American engineer by the name of Willis Carrier. The machine at that time was called "Apparatus for Treating Air".
the process of treating air to meet the requirements of a conditioned space by controlling its temperature, humidity, cleanliness, and distribution.
Note that "ASHRAE was formed as the American Society of Heating, Refrigerating and Air-Conditioning Engineers by the merger in 1959 of American Society of Heating and Air-Conditioning Engineers (ASHAE) founded in 1894 and The American Society of Refrigerating Engineers (ASRE) founded in 1904."
That said, "air conditioning" or "A/C", in lay usage almost universally refers to apparatus for cooling air. This Google Ngram shows that the modern inclusive term HVAC didn't begin to become common until ca. 1970.
ASHRAE defines HVAC system somewhat inconsistently as follows:
the equipment, distribution systems, and terminals that provide, either collectively or individually, the processes of heating, ventilating, or air conditioning to a building or portion of a building.