Hijab is not cultural.  It is religiously mandated in Islam.  Daleel (evidence) for this exists in the Quran, the Hadith, the custom adopted by pious Muslims and the consensus (ijma) of the scholars (Islamic ulema).  The position is very clear cut. The hijab is mandated in the Quran.
Quran 024.031 (typical translation of meaning):
"And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards Allah, that ye may attain Bliss. "

However, the verse is much clearer in Arabic.  The Arabic word Khimar (e.g. a head covering) is used.  The verse specifies how the head covering should be used.  For example, one cannot just wrap one's ponytail with a cloth and sling it behind oneself. The head covering must actually not only cover the hair but extend itself to the bosom area as well. 
Hadith clearly show hijab is part of Islam:

from Umm Salamah who  said: "When the aayah '. to draw their cloaks (veils) all over their bodies.' [al-Ahzaab 33:59 - interpretation of the meaning] was revealed, the women of the Ansaar came out looking as if there were crows on their heads, because of their clothing." (Sunan Abi  Dawood, Kitaab al-Libaas, Baab fi qawlihi ta'aala: yubneena'alayhinna jalaabeebihinna).
The author of 'Awn al-Ma'bood fi Sharh Sunan Abi Dawood said, commenting on this phrase: "Their veils were likened to crows because of their black colour."

It was how  Sahabiyyat  (female companions) practised Islam.

It is important for us as Muslims to remember the following hadith Sahih Bukhari Volume 1, Book 2, Number 8: Narrated Abu Huraira: The Prophet said, "Faith (Belief) consists of more than sixty branches (i.e. parts). And Haya (This term "Haya" covers a large number of concepts which are to be taken together; amongst them are self respect, modesty, bashfulness, and scruple, etc.) is a part of faith."
For a Muslimah it is clearly an part of faith to use hijab.
Indeed, for a Muslimah who covers to obey Allah(swt) and out of sincerity and love for her Lord, she indeed receives some wonderful gifts for that effort during her lifetime. Sahih Bukhari 8.138 Narrated by Abu As Sawar Al Adawi: Imran bin Husain said, "The Prophet said, 'Haya' does not bring anything except good.' "...
In fact it is only over the last hundred years or so that some Muslim women have uncovered themselves. Alhumduillah, some Muslim women today in the West are slowly beginning to lead the way back to correct Muslim attire despite sometimes daunting obstacles.  May Allah (swt) reward those who sincerely seek His pleasure.


Sahih Muslim, Book 001, Number 0270: It is narrated on the authority of Abu Huraira that the Messenger of Allah (may peace be upon him) said: Islam started as something strange, and it would revert to its (old position) of being strange. so (give) good tidings for the stranger.

And Allah(swt) knows best.