Does a colder CPU perform better?
If a CPU produces any errors at all in computations, we consider it "broken". If the CPUs temp specification gives it's normal operating temp range as 0 ~ 95 ˚C (for example) it will produce no errors over this entire range.

However, in general, semiconductor devices will draw less power at lower temperatures, so, ironically, if you spend some power to cool them, they will consume less power. This is usually not a very important attribute except to heat sink and power supply designers.

Digital logic propagation times usually decrease with decrease in temperature, i.e. the gates get "faster". Theoretically, you could increase the clock frequency of a CPU if you were to keep it cooler compared to when it was hot. This would of course make your computer faster. But you can't get fewer than 0 errors ;)