It's possible, just remember, condensation forms whenever something is below ambient (room) temperature. If you run refrigerated air into your rig, water will form in there and thats not good for electronic stuff. I read where some people are coating their MoBo's and cards and stuff with silicone to protect it from condensation. Might be worth a look, at least.
its been done. I believe these were the orignal way to supercool computers. But as TT120 pointed out, condensation is a big prob. Get a watercooling rig from danger den and be happier and get the same cooling, for cheaper!
funny thing you mention that, i've been considering the exact same thing. i live in southern part of illinois and temperature got a little warm this weekend and my computer temps were up about 5 degrees celsius and that was just enough to make my system unstable. it is bad enough my duron 800 won't hit a gig, but to add insult to injury i'm now a slave to the ambient air temperature.
seems from what i've read when you use a refrigerator not only do you have to worry about condensation on the mb, but also on the water hose too. once i can scrape together the cash for a mini fridge i think i'll be giving a refrigerator cooled setup a try. let us know if you decide to put that extra fridge to good use!
I think that one of the problems with this idea is that the motor on the refrigerator can't cope with the constant heat produced by the computer...it's designed for something that will stay relatively cool once you cool it, not something that will heat up even when you do cool it.
Now, I'm not positive that this is the case, so I would look into finding someone who has been successful with this, and has been for more than a couple of months or so...as the motor might just not ever shut off, and that would probably wear it out a bit, don't you think?