Hey, I'm an electrical engineer with a background in robotics and control systems. I usually work with motion control, but also have experience with temperature, humidity, light, etc. Been keeping miniatures for a couple years after getting hooked on dendroboard. I saw this thread and thought I should jump in!
Others have touched on it already, but cooling is complicated. Temperature, pressure, humidity, and airflow are all related. Try to control or modify one and you probably mess up two others! It is possible though.
The first step is to limit the amount of cooling you need. Drop the ambient temp of the room as much as possible (or use a basement if you can), then insulate the tank as much as possible. Minifridge is a good start, you can also look at wine coolers since they tend to come with a glass door. Cork and great stuff expanding foam are also great insulators, so backgrounds made from these materials will help.
Peltiers really have two problems for this application.
1) They are small compared to the size of the tank you are trying to cool. So they have to remove all the heat leaking in from all the walls of the tank. This is why you need to insulate those walls!
2) They are not efficient coolers. This means that It takes a large amount of electrical energy to remove a small amount of heat energy from the tank. You can think of a peltier cooler like a heat "pump". You give it some electrical energy, and it "pumps" some heat energy out.
Evaporative coolers, and refrigerators can both be more efficient.
Heat pump and refrigeration cycle - Wikipedia
I'd recommend looking into aquarium chillers (especially used) as a cheap way to get a lot of cooling power. How you use all that cold water to cool down the air without messing up humidity is another problem!
Hope this is helpful.
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