While they are hearty creatures indeed, cold weather will kill bed bugs. Bed bugs die after four days at 0°F.
In fact, going to an extreme temperature in either direction is a well-known way of killing bed bugs. That is why steamers are a good tool for bed bug extermination. Bed bugs are thought to be growing more resistant to bed bug insecticides so manipulating temperature shows a lot of promise as an extermination method. The challenge is finding ways to develop techniques that are practical and non-destructive to your home and belongings.
It’s not practical for somebody that lives in Florida to keep their mattress and box spring at 0°F for four days. However, in some climates or at certain times of the year, this is entirely practical. If you have access to a large enough refrigeration unit or freezer, treating belongings of various sizes is practical as well. As long as you can keep the temperature low enough for a long enough time, you can kill bed bugs with cold.