Depending on the location, it might be the case that the area treated causes numness of a nerve's dermatome (the area of the skin that is allowed to feel touch and pain) even though the area is in an adjacent area but not the area of treatment. This is similar in patients with back problems such as herniated discs and have nerve irritation in the spine which can cause leg pain, except in the case of CoolSculpting, numbness can be created temporarily.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice. The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs.