You are referring to what is known to engineers as adiabatic humidification where no heat source is required to get the water into the air as opposed to isothermal humidification, the more common humidification used in museums where heat is required. This technology is the same as is used in fire mist suppression systems. I recently did quite a bit of research into adiabatic humidification for possible use in our new Arts and Education Center because I was interested in possibly saving energy because isothermal humidification is so energy intensive and expensive. Just do a web search on "adiabatic humidification" for more details on how it works, but here is a quick summary:   http://www.dac-hvac.com/ask-rick/ask-rick-what-is-adiabatic-humidification/
This is even better, but more technical:  http://www.dristeem-media.com/literature/HPAS_White_Paper_Adiabatic_Basics.pdf

In short, humidification is usually required in cold climates where the air is dried out by heating. However, water micro-droplets are not absorbed by cool air very well. If water is added as steam, it heat ups the air as it is introduced. When no heat comes with the water, the air has to be preheated so some of the anticipated significant energy savings are spent heating the air. However, the main problem with using it in museums is more logistical. The water has to be treated to remove all minerals before it is "misted" or a fine white mineral mist will deposit in the ducts, clog up the mist generators, and be deposited on the artifacts. Museum facility managers and staff know how to maintain and service isothermal humidifiers, and in fact the Nortec models have a nice throw-away canister to get rid of the minerals that are deposited in an isothermal humidifier as the water turns to steam. Adiabatic humidifiers require an entire water conditioning setup to maintain and service and such water treatment is not inexpensive. In addition, most museum facility staff do not know how to maintain water conditioning systems (sure, they could learn). 

I am sure the engineers at DriSteam or some of the specialized adiabatic manufacturers will be glad to calculate the price for purchase, installation, and operation of adiabatic humidifications as compared to traditional isothermal humidification. In fact, I talked with one but never had them go through the calculations. If you do, just make sure they include the cost of pre-heating the air and treating the water. After all was said and done, we decided to stick to isothermal humidification like we have in six other museum buildings. The manufacturer we checked with was in Arizona where it is hot and dry unlike Vermont where it is cold and dry. The physics of diabatic humidification probably makes a lot more sense in a hot and dry climate. 

As an aside, we did choose to purchase and install a natural gas powered humidifier for the non-gallery two-thirds of our new building. They are at least double the price of an electric humidifier, but they cost 1/10 the cost to operate with the presently low natural gas prices. The payback was about 3 years. However, they only come with a relatively large minimum output and the HVAC engineers I consulted with claimed that they do not control RH as precisely as electric humidifiers. Even though museum professionals are now considering wider safe humidity ranges even for our finest works of art, the museum HVAC engineers still recommended electric humidifiers for art gallery applications, at least in the Northeast US.

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