From the fresco of Julius Terentius from Dura-Europos

The Pilleus Pannonicus or Pannonian cap is a late Roman military hat made of felt or fur. It's believed that they were often made of persian lamb (shearling) or astrakan. The hat Magnus wears is constructed in a pillbox style. It's made of shearling from an old coat and lined in a canvas weight linen. Note that the texture of the hat in the 4th century Roman coin closely matches that of the shearling of Magnus's hat.