It’s not a cowboy hat, it’s a U.S. Parks Service hat since he’s officially representing that dept. Not sure if protocol requires that he wear it, but it well might.
Read this article and see if you still feel the same, that it’s not a cowboy hat.
http://voices.washingtonpost.com/federal-eye/2008/12/whats_with_salazars_hat_and_bo.html