Balaclava

A balaclava is a close-fitting garment that covers the whole head and neck except for parts of the face, it is typically made of wool.

Rubeus Hagrid was wearing one of these when he talked to Harry Potter about why he wasn't in class (Herbology had been cancelled because of the snow). Hagrid also had the very same balaclava perched on top of his head when he burst into Albus Dumbledore's office only hours later to say that he was prepared to swear that Harry was not the heir of Slytherin in front of the Ministry of Magic.