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Does an ultrasonic air humidifier use energy less energy than a steam humidifier?

There are a couple different types of indoor air humidifiers. Most notably, the naive steam humidifier with a [heating element](https://en.wikipedia.org/wiki/Humidifier#Heating_element), and then [ultrasonic](https://en.wikipedia.org/wiki/Humidifier#Ultrasonic_humidifiers) humidifiers.

Now, heating water to create steam obviously takes quite a bit of energy. The ultrasonic humidifiers take less electricity, because they just "sprinkle" tiny droplets off the water surface, leading to a cool mist.

So my question is this: **Is there an actual gain in overall electricity usage, if we assume that the house is heated with radiators (which maintain a steady temperature)?**

My intuition would be that the (relatively) cool droplets from the ultrasonic humidifier suck off heat from the surroundings while "turning into actual air moisture". Maybe this air cooling effect equals the amount of extra energy that would have been required to produce the same humidity level with a naive steam humidifier, effectively nullifying the supposed energy gain of ultrasound humidifiers (in this setting)?