2003 Hummer H2 air suspension

Is this an automatic "air" suspension with Air Bags?

yes it it is automatic with rubber boots that adjust the height of the truck. It comes factory on the h2

if that is the case, I believe you have condensation in the air system, common in the winter time, specialty in high humid climates, I'm not too familiar with the air system on the Hummer, I am semi truck mechanic, but it is a very common problem on the Big Truck equipped with air brakes and airbags, does it have an air tank? so you can drain it and remove the water, the only other thing you can do to service the air system, is to locate the air pump and remove the supply line to the airbags, insert about 2 ounces of "air brake system antifreeze" easy to find at any truck stop, or a real part store, this would help removing condensation in the system, and condition it. which may be causing your problem