Will extremely cold weather affect ECM on stored '88 corvette?

You stopped before asking a question. What happened when the ECM replacement was put in? Computers get old, and when they are left in the cold, (how cold was it?) they contract, then when warm expand. This movement at times will break connections on the computer boards. Normally electronics work better in the cold, but the connections can become open (broken or separated) and cause a malfunction. Any computer circuit board, used or not is susceptible to that type of damage. If you store your car in the winter in the cold garage, perhaps put a 100 watt old style bulb under the hood to add warmth. Be careful it is not touching anything so it will not start a fire. Use an inspection or wire cage to put it in. Place a cover like a mover's blanket over the hood for added insulation. Warning though, cats and rats also seek warmth on cold winter nights. Cats are no bother, rats like to eat electrical wiring.