Yes freezing temperatures do kill cockroaches.
If you have a house that has cockroaches in it you can shut the heat off and also the water and then allow the house to remain at freezing temperatures for a few months.
It takes prolonged cold temperatures to kill the cockroaches but it can work.
I once did this to a house I had rented out.
The house got cockroaches and the renters moved out.
I decided to leave the house cold during the sub freezing temperatures we had for a few months and during those few months all the cockroaches died.
You can also spray cockroaches with bleach or ammonia which will also kill cockroaches.
Or use some Raid Roach Spray which also kills the roaches.