Two explanations (found on the web) about it that say almost the same thing and perhaps clear up doubts...
One... To conserve rubber North American Mustang fighters are equipped with wooden wheels during final stages in assembly. Rubber tired wheels are put on when the plane is ready for flights test.
Two... Wooden wheels are attached to a P-51 ("Mustang") fighter plane so it may be moved around the ramp at the Inglewood, California plant of North American Aviation, Incorporated. When it is ready for flight tests, regular landing wheels with rubber tires will be substituted.