Perhaps the most famous mummy found with his hat in tact is the 2,000 year old body of a man found in a Danish bog in 1944. He was/is wearing a cap sewn from eight or nine pieces of leather with the fur side inmost and a conical crown with a band along the lower edge and a chin strap.
Scroll down in this HAT FACTS section to the "Everyday guy in Europe 2,000 years ago" for a look at an illustration of this cap as it was worn back then.