I have a long and somewhat rambling post about this general issue:

• Do the ubiquitous photos of Iran prior to the ascent of Ayatollah Khomeini (showing the country as very Western and cosmopolitan) accurately reflect the mores and sensibilities of Iran's general population or were such "indulgences" largely limited to the more privileged and urban?

I can't speak for the medieval period exactly, but I can speak with confidence that in the 19th century urban and rural Ottoman Empire the norm was certainly covered hair (for minorities as well as Muslims, for the most part). The same is true throughout the 20th century but across the Muslim world you see more elite, urban women increasingly uncovering (the proportion varies greatly between countries, and does not really apply to the Gulf States to my knowledge).

"Hijab" can mean different things to different people, so I'll specify that I'm talking minimally about hair coverings. There has, very unfortunately, not been a good history of modern Islamic dress, but the consensus is that "the modern headscarf" starts in Egypt in the 1970's. This headscarf is associated with political Islam. It's often called "Al-Amira" in the Arab world and the Türban in Turkey. It's hard for me to describe exactly how it's different, these trends don't really apply to the Gulf States and are noticeably different in Iran (where political Islam was and is often associated with indigenous black chador). Here's a contemporary survey that captures some of the differences between both styles and countries.

Number 1 is the proper sky-blue burka really only found in Afghanistan. Number 2 is the niqab/abaya combination found in the Gulf States and often symbolic of affiliation to Salafism. Number 3 is the chador traditionally found in Iran. Number 4 is the "modern headscarf" that I mentioned above. Number 5 is one variety of traditional headscarf (one of many--indeed, Ottoman elite dress at times looked more like number 2 but also villagers in places simply covered their hair but not even their neck), but I think the picture is not really trying to represent a traditional dress but a modern, relaxed headcovering. With the hair showing in front slightly, it's commonly warn by urban elites (and visiting westerners) in some more conservative countries. Here's a picture that I love from contemporary Iran, showing that style in action.

But the point is, while women didn't necessarily wear styles most people think of when they think of contemporary styles, they generally did cover their how. How they did it varied largely based on place--not only by country, but styles varied in many places hugely by social class (with elites through the 19th century generally being more covered and then by the mid 20th century urban elites being distinctively less covered, as regimes from Tunisia to Iran encouraged their elites to "modernize" and adopt Western dress) and whether one lived in the village of the city. In the countryside, women generally did and do cover their hair, though even there styles vary dramatically not only by time but place. Those old pictures from the 70's represent a minority, not a majority. Today, in Turkey, likely the least covered country in the Middle East/North Africa region (besides Israel and Lebanon) only 20-35% of women are uncovered (depending on the exact survey). Despite the hype, this is almost certainly the high point for these figures.

In short, I can't say exactly how Muslim women dressed in the Middle Ages, but I can say that in the 19th and 20th centuries, most Muslim women in the Middle East and North Africa covered their hair in some way, though (for the most part) in a different style than today. The styles have changed but the fact that a majority have covered their hair has not. All those pictures in those albums tend to represent a thin, secularized urban elite, not an absolute majority of the population. (Ping: /u/TheVegetaMonologues who asked a similar question).

Follow-up question:

We see these albums posted often, to show us how different the attitudes of the muslim world were toward women only a few decades ago, but I've heard people say that outside of Kabul, for instance, Afghan women lived much the way they do now. Are these pictures really indicative, or was the more familiar, secular, more "western" society depicted in these albums an isolated, urban phenomenon?

Another follow-up: what is the history of head covering in Christian Europe?

You still see older women covering their hair in Catholic and Orthodox countries, and I remember seeing head coverings in medieval depictions of women in Northern Europe - was this common throughout society? And when does it become less common?

There is evidence to suggest that women in the medieval Arab world did typically don some form of veil, a practice that seems to have carried over from pre-Islamic times. In chronicles and polemic, the veiling of women becomes a marker of difference between the civilized or righteous Muslims and the opponents of the moment: the Greeks, the Franks, renegade sects like the Qaramita. Crusades-era chroniclers are horrified by the scandalous dress of Frankish women; they are more allured than scandalized by how even married Greek (Byzantine) women go to the markets with their faces and hair uncovered, their beauty on display.

Of course, the polemical nature of these sources has to be qualified. It was fairly typical for women in the Greek East and Latin West to wear some form of head covering in public, too (actually, Latin canon lawyers repeatedly take up this issue with respect to independent holy women, worrying that their particular version of head covering is illicit appropriation of a monastic habit). Second, these sources relate an ideal, not necessarily a reality. They don't tell us how factors of location, class, and time may have affected things. The ideal medieval Muslim woman was to live in full seclusion, a "privilege" accessible only to rich men who could support them. Veiling was a way to extend that seclusion into public. But does this mean that poor women were out and about in veils? Or was seclusion itself a value only to those who could afford it?

A good ecample of veiling at the elite level comes from the fascinating 13th century Spanish (Christian) manuscript called the Book of Games. It's somewhat famous for depicting Muslim men with a range of skin tones, but it also pictures both Muslim and Christian women--all with some form of head covering and their faces free.

I'm not familiar with any scholarly attempts to piece together what medieval Muslim women thought about veils or no veils, in al-Andalus or Egypt or Baghdad, in 700 or 1000 or 1400. Were veils a price to pay for an active public life of buying and selling, founding Sufi lodges, studying or even teaching at a madrasa? Were they a fashion accessory, loving color coordinated? Judging from the grumpiness of male legal scholars with a bit more piety than perhaps necessary, not all women bought into the underlying philosophy that veils took them "out of the world" and hid them in plain sight. From a 10th century Andalusi hisba:

Yahya was asked about a kind of sandal or flip-flop. Are shoemakers forbidden to make them? Because women look for these mules on purpose, with the intention of wearing them when going through the markets. And it so happens that, if a man is absent-minded, when he hears these chirping sandals he raises his head.

And another hijab history question (just not to start a new thread), what's the history of hijab use during olympics? Did female muslim athletes never used hijab before? Or were they never allowed to participate in the competition until recently?

As a lot of the other answers have mentioned, this is a tough question to answer because of just how diverse 'medieval Islam' could be taken to be. What can be said with certainty is that head coverings of various sorts have been used both at an elite and popular level throughout Islamic history, and the practice actually pre-dates Islam, but it's important to keep in mind there was a remarkable level of heterogeneity. What can also be said with certainty is that the ways in which people relate the importance, and the style, of head coverings, has changed dramatically and had little consistency across classes, cultures, and geographies. Again, as others have pointed out, the contemporary use of the Niqab and Hijab, and the various styles of headcoverings, are relatively new phenomenon tied to the rise in 'political Islam' starting in the 1970s.

Anecdotally, when I first visited the Middle East a little over ten years ago, it was quite rare to see a child wearing the full hijab-style covering where as now it's quite common, and you see mannequins wearing them in the downtown store fronts even in a relatively liberal place like Amman.

Back to answering your question, it's also a tough one because we simply don't have a lot of solid sources about how people in general related to head covering outside of elite circles in the period you're wondering about. This elite/non-elite distinction is an important one, and we can be quite sure that whatever we know about veiling in elite circles doesn't also hold for non-elite rural communities. There's a great book looking at Iranian sexual politics by Janet Afari where she suggests that veiling in any kind of sense that we'd understand it today would have been quite rare in rural Iran before 20th century given the impracticalities of full covering in an agrarian context. It goes a lot further looking at sexuality in Qajar Iran and makes some really compelling arguments that in a lot of ways people were much more comfortable with ambiguity in gendered contexts than they are today. Other historians have suggested that decline in comfort with ambiguity was actually a direct result of colonial ideas about order and morality being imposed and taken up by local actors who saw in European structural intolerance a path to modernisation. There's another interesting book by Gregory Starrett called 'Putting Islam to Work', which suggests that the politicising of Islam in the 20th century (of which the veil became a central discourse, and obviously still is) was largely promulgated by secular states' (think Egypt's nationalisation of al-Azhar) attempts to control Islamic discourse for their own nation and state-building purposes, and once that had been completed, Islam as an idea was open to be re-politicised by 'Islamist' anti-state forces opposing their vision of society. A more general point is that much of the discussion about proper head covering in the last few decades is intrinsically tied to the rise of mass media and politics, thus giving the ability for certain sections of society to set normative standards for behaviour and practice through them. These are all very modern developments, and it's important to remember the very different social and political context of the medieval Islamic world.

I digress, but going back to Afari's point, there's no reason to think this (the rarity of full coverings in rural areas) also wouldn't be true of other places in the Middle East, North Africa, or South and East Asia. I'd love to pull out some quotes but I seem to have lost them; either way the general thrust was, well, who wants to wear a Niqab while working in the fields?

So, to sum up: no, it's very unlikely that there was a normative standard for head coverings across the medieval Islamic world, and the fashion (or practice, depending on how you want to think about it) would have been so various and heterogeneous as to preclude any general claims about it, and it's very likely the majority of Muslim women did not regularly use the kinds of modern coverings, and if they did, the context of it would have been quite different.

I'd like to add another question, in Assassin's Creed Revelations set in early 16th century Istanbul, ordinary women on the streets are shown wearing something similar to a niqab. How likely would this have been?

The first image seems to be misdated. It looks to me like the date reads Friday, 2 Esfand 1336, which corresponds to 21 February 1958, not the 70's.