Padded Coif

 This coif is padded as it is designed to be used as an arming cap under a metal helmet.

See the previous post about arming caps

This style of arming cap is typical of the Medieval period from 12th Century onwards

This style of arming cap was also worn by medieval peasants as an outer layer as well as under a helmet.

Balaclava

.A Balaclava is also called a Ski mask

Originally a knitted wool item they are now made of any stretchy material that will keep you warm and make the Balaclava fit snugly to the head and neck

Designed to cover the whole head and neck, exposing only eyes, nose and mouth (most of the time) it's designed for maximum warmth in cold conditions

The name Balaclava comes from the battle of Balaclava which took place in the Crimean war in 1854. They were never actually worn in the war as, despite the need by British troop fighting in the bitter cold, the headgear never arrived in time. Still, the name stuck.

The Balaclava was also known in the 19th century as the Uhlan cap worn by Polish and Prussian soldiers

Hat With Badge

 This black fabric hat is a basic bag form with its edge rolled back on itself to form the brim.

It could fit many periods from Medieval or older to the present day.

Decorated with a metal badge, it gives it a more medieval feel, although the fabric is far from authentic for the period.

Red Decorated Sombrero

The Sombrero the traditional hat of Mexico

A Sombrero in Mexico is any wide-brimmed hat, although for most people outside the region it is also a hat with its brim upturned along its edge.

Its main function is the protection of the head and shoulders from the Sun.

Some like this one can end up highly decorated and are used by Mariachi folk music performers.

This I believe is a full Sombrero but in Mexico there are many types with names suchas Quinciano, Diechinueve, Veintiuno, Veintisiete, Traditional sombrero or modern sombrero.