I read on http://www.nirschl.com/elbowten.asp:
Ice is an important element in the healing process and should be used any time signs of inflammation or intense pain are present, no matter how soon or long after the injury. Post exercises ice is also recommended and may be done in conjunction with sensory level electrical stimulation to promote pain and inflammation control. The benefits of ice include a reduction in pain, inflammation, and muscle spasm. Time of ice application ranges from 15-30 minutes. Icing over 30 minutes may cause frost bite. To protect the skin a thin layer of cloth between the skin and ice is worthwhile. Avoid icing the ulnar nerve directly when icing the elbow.
Why should one avoid icing the ulnar nerve directly when icing the elbow?