Yeah liquid nitrogen would be better but you can't carry all that much. Just like nitrous. What could be done with Peltiers is to take an existing aftercooler and extra chill the liquid. There have been some advances in the technology, for instance a 40mmX40mm pad can dissipate up to 575 BTU(although you'd probably only see 2/3 of that in practice) Still it should be possible to drop coolant temp by 20 degrees or so allowing for the aftercool to chill the air better maybe more. The issues are how much the electrical system can handle. I think it should be possible but does it really matter.

For instance people before a 1/4 will put ice/ice water on/around/in the intercooler to chill it better, how much of an impact does this make?

Overall we could use something other than Peltiers to achieve the same effect but they are reliable, simple, long term and most of all small. The goal is to use the peltiers to enhance the existing cooling not to entirely replace it. Just some thoughts. It's probably something I'll experiment once I get my SC. Mostly curious about how much impact the cold air can have. Of course there will be challenges to make it work within the electrical system but it's solvable.

 

I think Mugen estimates a 1% increase in power for each 10 degree decrease in IAT. I don't know if that is C or F...

As many have already stated, for there to be any benefit, you would have to be able to reduce the temperature very efficiently. If your cooling device increases load on the alternator, then the alternator will put more load on the engine.