Ice, Ice baby
That has been done, but badly. The company who made the car cooler engineered it after drinking too many Pearl beers and they created something that could keep cold things cold for a while but could not make warm things cold. But that certainly didn't stop them from producing and selling thousands. Nosireebob.
These things are really amazing when they work at their best and when they're kept within their limitations. I know it is hard to get your mind around a concept like the thermoelectric device at first. It was for me, too. The first time I worked with one I could not believe anything could move heat so rapidly. But similar to what Clint Eastwood said, you gotta know your limitations. That is really important. The idea that you could aircondition your house with several of these is folly. The idea you could aircondition a very small car or better yet a small pickup with several of these might be more possible, but still very unlikely and challenging. The idea you could (if you were clever and creative) build a small countertop icemaker is actually possible. In fact I'll prove it. Please look at the image below. That is a 1 inch diameter circle of ice about 1/8 inch thick and it took me about 5 minutes to make it. The ambient temp in here is 80 degrees...maybe 79 but the thermometer says 80. The cold sink was removed exposing the 1 inch thick aluminum spacer onto which I spread a film of water so I'd know when the freezing point was hit. The heat sink was set atop the fan and the fan was given about 1.5 inches of space between it and the top of my desk. The unit was started and within 5 minutes it had completely cooled the aluminum spacer (about 2.5 inches by 1.5 inches by 1 inch thick) to less than 32 degrees and had frozen the water I had dropped onto it at the start. The more water I dropped on to the spacer, the more it froze. And remember this is out in the open at an ambient temp of 80. I stopped at about 1/8 of an inch (which did not take long to build up). I'd expect a clever person could design either a small cube ice maker or better yet a flaker...that's where the real money would be had. After all, I just showed you a monkey can make ice cubes with one of these. A countertop ice flaker could be sold quite easily because flaked ice has always been special. And ice flakers are not cheap...go price some Scotsman flakers. You can part with $5,000 easily. The key with that type of machine is to separate the ice from the chiller before it becomes hard. You have to use either a screw blade wiping a cylinder or something similar to separate the ice just at the point where it freezes and then move it up and out of the way so more can follow it. But I believe it could be done.
Now here is the other thing I haven't told you yet. If you reverse polarity, what originally was the hot side now becomes the cold side and what was originally the cold side becomes the hot side.