Research suggests there are few risks associated with cooling therapy for children with hypoxia if done correctly. Trials seem to suggest there are more positive than negative benefits.
The most common side effect that appears to be a risk is sinus bradycardia, known as a slowed heart rate. However, it is not a life-threatening condition. It can also be treated depending on its cause and severity. The biggest risk of cooling therapy, it would seem, is not doing it at all or not doing it correctly.