It is unclear what "hat and scarf combo" is being referred to here. Arabs, especially Bedouins, wear a wide variety of headgear. The below answer will describe a few different types.
1) Kuffiyeh (كوفية): This is typically worn by males and is composed of a cloth like a handkerchief, usually with a plaid design and colors like white, black, and red, and a black cord called an 3aqaal (عقال). The cloth is first placed on the head and covers most of a person's hair, then the black cor in tied around the head to secure the cloth. There are several different styles of kuffiyehs with different types of fabrics and colorations, usually indicating a local or tribal difference. Most Emirati Sheikhs wear white kuffiyehs, for example, while Yasser Arafat famously wore a black and white plaid design.
2) Hijaab (حجاب): This is exclusively worn by women and is headscarf the covers all of a woman's hair in a way very similar to a nun's habit. Settled Arab women also often wear the hijaab.
3) Burqa (برقة): This is also exclusively worn by women and only in certain Bedouin communities. In addition to the hijaab, this will cover parts of the front of the face, either with a metal mask, jewelry, or sheets of cloth with wholes for breathing ().
4) Masaar (مصار): This is a turban worn traditionally by males of Oman. It is made of a scarf that is wrapped around the head several times and tends to appear flat-topped as opposed to Sikh turbans which have a rounded top.
5) Ghotra (غترة): Also called a shemaagh (شماغ) or hamdaniyya (حمدانية), the ghotra is typically made of a thicker cloth than the kuffiyeh and is a similar scarf-shape to the Masaar. However, unlike these garments, the ghotra covers both the hair and the chin with some fabric covering the upper chest. Like the kuffiyeh, the cloth is usually in a plaid design with coloration being determined by tribal affiliation.
A long thin scarf is typically called a "scarf" or a "skinny scarf".
It can be called a cap or a scarf.
It's still just called a scarf, or a men's scarf if you are being super-picky about it.
A boa
A huntsman's is called a stock
It can be called a cap or a scarf.
fanon
rebozo
The small blue scarf is in the middle-left portion of the image, slightly to the right of the orange and yellow striped scarf. It is placed on a mannequin that is wearing a blue and white striped shirt.
A fichu
A scarf without ends is called an infinity scarf because it is a continuous loop without distinct ends. It can be worn by looping it around the neck without any need to tie it or wrap it like a traditional scarf.
Well why dont you wear a coat and scarf next time you go to the beach and find out?