I'm just learning about watercooling and have been thinking about possibilities for a sub-ambient system.
You've got to separate the components that need protection from condensation (motherboard, etc) from the rest of the environment otherwise you're going to be continually working to remove moisture from the air. And you have to consider a hobbyist's ability to actually build a chamber that is completely air tight. Its unlikely that someone could affordably build something that can be made free of moisture when the system is setup and be expected to remain so indefinitely. Its probably better to have a setup that lets you remove all moisture initially (say prior to system startup) and then be able to deal with any moist air that enters the enclosure through imperfect seals.
Vacuum - That was my first thought, but if you are actually evacuating all of the air from the chamber how is heat being transferred from all of the components that aren't physically connected to a cooling loop? Spinning a fan around in a vacuum doesn't do anything. You could deal with this by immersing the system in a non-conductive liquid (the infamous mineral oil cooled system) leaving some space at the top of the chamber for expansion of the liquid. You'd only be evacuating the air from that extra space.
Dehumidifier - there are small Peltier cooler-based dehumidifiers that might work. Again it might be best to put the system under liquid, keeping the amount of air in the enclosure as small as possible to limit the amount of water that needs to be removed. They work by making their dehumidifying elements colder than the surrounding air so water condenses (and I believe typically freezes) on them. They would need to remain running or the water will re-enter the air. You could also try using a dessicant to remove moisture but it would take time and require replacement as it absorbs water.
Purge - I work in a lab and we use air from which all moisture has been removed. You could use that to purge the chamber prior to cooling down the system and then do further purges if leaks allow moisture into the chamber. Other gasses are also possible. The problem is obtaining the gas cylinders or gas generator. I have worked with systems that remove moisture from air fed into instruments but i don't know that they are really drying the air to the extent that would be necessary for this purpose.
Liquid Immersion - As mentioned above you could use liquid immersion to reduce the amount of air in a chamber that had to be removed. It might be possible to avoid the need to worry about humidity/condensation all together if the system is under liquid (lets just say mineral oil). Mineral oil covering the system would prevent water from condensing on it. If the container is open, the only places you'd get condensation are on the top of the oil or more likely, the cooling loop before it enters the oil. If the loop enters the oil from the top the water will run down the tubing and into the oil. It (and any moisture condensing directly from the air on the oil) is going to sink through the oil and settle at the bottom. If its at the bottom of a tank, won't be disturbed and will stay there that's fine. But if small amounts are going to settle on the surfaces of the motherboard, etc it doesn't matter that they SEEM to be under oil, there will be water on them. I don't know if you could effectively route the flow of oil in the tank so that water settles safety on the bottom of the tank and never contacts the system. If the tank is sealed it might be possible to start the cooling loop (but not the computer itself) along with a system that circulates the oil slowly in the proper direction to send all condensation to the bottom of the tank. Once no more water condensed out of the air the circulation system could be adjusted (or an alternate system turned on) so that the oil still circulated for cooling purposes but in a way that any small amount of water on the bottom of the tank was not disturbed.
just some ideas...