This is a wool felt Tyrolean Hat
I have posted information about this style of hat before, so won't go over it again other than to say the name Tyrolean hat comes from Tyrol a region in Austria
Can also be known as a Sepplhut
Although Sepplhut can also be taller, pointier and have wider brims, the distinctive feature of Sepplhut seems to be wool felting and the cord around the base of the crown
A Christmas gift