Q.  Can one add water to a cold water humidifier on Shabbat when it is close to turn itself off because the water is bellow the on limit? If you are allowed why is it it different than a vaporizer?
A. The basic difference is that a steam vaporizer or warm-mist humidifier uses electricity to power a heating element. It boils water and creates steam. The steam cools down before it leaves the machine and enters the air. When you add water to the vaporizer that water will be boiled on Shabbos and therefore it is prohibited.
There are three basic kinds of cold water humidifiers. One type uses a fan to draw air through a wet wick (or wick filters) and then release the vapor into the air. Another uses ultrasonic vibrations to disperse a cool mist of water into the air. A third kind uses a disk submerged in the machine that is rapidly turned. As it moves, it breaks up the water into tiny particles that can also be release into the air and also inhaled.
Since these device are already on before Shabbos began and constantly working, and no boiling of water is involved their use is permitted.
Horav Shlomo Miller’s Shlit’a opinion is that although the Melacha of Zoreh (winnowing, as in separating the chaff from the grain using the force of wind) could be involved, it is similar to the spray of aerosol cans into the air, that many Poskim permit.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a