Thanks for the advice. I sorted out the problem which had two solutions:

1. In Skin Editor, I selected all the mapped mesh then EDIT > SET SKIN, and the texture appeared on the model. I'm not sure why I have to do this if the skin has already been set in the model editor EDIT > MANAGE SKINGS > SET SKIN. But it works.

2. Sometimes the texture does not appear on a model due to video settings. I went to FILE > PREFERENCES > VIDEO OUT and changed the GXL option. [This is a general issue not just related to importing MD2 files. What is GXL anyway?]