The colder the air - the denser the air. The denser the air - the more oxygen it has. That's why NOS makes power. It is very cold and when it is combined with air, fuel and spark it makes a very big explosion. That larger than normal explosion is what is making more power. I think the formula is something like 1% horsepower gain for each 10 degrees drop in temperature.

That's the same reason to use an intercooler in a supercharged/turbocharged application. Pressure heats the air and an intercooler reduces that heat. You can see a very large drop in pressure if your intercooler is not large enough but it can also have a negative affect if it's too big.