If the roaches are in a house or building with no heat they will freeze to death if the roaches do not move to a warmer place.
Usually though the extreme cold will cause roaches to leave the cold house or cold building and go find somewhere warm.
If the roaches are unable to find a warmer place then they will freeze to death.
I had a roach infestation in a house before and I turned the heat off and moved into another place for the winter and when I came back the roach infestation was gone and I found some dead roaches on the floor and counter because they didn't leave the house and froze.
So in extreme cold the roaches can die.
You can also use soap and water in a spray bottle to spray the roaches directly and the dish soap and water will kill the roaches almost instantly because the soap and water suffocates them.