Winter stress could include not only cold temperatures, but also dry conditions. Young trees should also be watered once or twice during dry winter conditions. Stress is a compounding factor. That is each stressful condition builds upon the next slowly weakening the tree. There is a point reached in which the plant cannot over come the problem and dies.
Supplemental water is one factor to help reduce stress build up.
In the case of native trees most of them will be fine. They are in a dormant state conserving as much of their resources as possible. Most native trees will not die unless these conditions continue for some time in the future. It is our responsibility when possible to help the trees by reducing environmental stress.