Is it possible for cold therapy devices to cause skin and nerve damage?

Yes. If your speaking about a constant cold therapy device such as one of the ones which circulate cold water continuously or even a simple ice bath or ice pack, the answer is yes. Take care to protect the skin and subcutaneous structures from damage by icing through a towel or facecloth, and limiting ice to 10-15 minutes. Consult your doctor, pt or atc as to the best method for your particular problem.
Cold therapy. Exactly what kind of cold therapy devices are you asking about? Please be more specific so help can be given to you.