How much time can a person be in cardiac arrest and survive with little to no brain damage when they are in icy?

Varies. Less than 5 minutes is the normal temperature answer. There have been anecdotal events of people that have been hours in icy water that regain consciousness with no brain damage, it is thought to be due to a decrease in metabolism. No real time known due to the fact that we can't really experiment to find out, and we only see it when it happens in real life. Not so common.