Does cold therapy penetrate deep enough to treat a herniated lumbar disc?

Yes. In most patients, cold therapy can help relieve some of the inflammation in the large muscles that surround the spine. Although the cold temperature associated with cold therapy does not reach all the way to the disc, it can help relieve some of the pain and muscle spasm that occurs along the muscles just underneath the skin layer.
It will not reach. The location of the disc but can reach the muscles that are responding to the effects of the disc herniation and will help control the muscular symptoms.