Medieval clothing was by and large heavily influenced from two sources: Persia and the Eurasian Steppes, which carried fashions over from China. These fashions then were usually disseminated into Western Europe via the Roman Empire ("Byzantine Empire").

Pants, originally, were seen in the mediterranean world as "feminine" and were even called "Feminalia" (which specifically referred to footed tights, called Anaxarydes in Greek). Ironically, as far as I know, women never wore them except for mounted female warriors from steppe cultures like the Scythians and Sarmatians - it was more of an insult towards Persian/Eastern Men and to Romans who dressed like them (until they became fashionable, of course, in Late Antiquity). And those pants were usually called "Saravara" since they were loose and not footed.

Long Tunics were worn by women for cultural reasons - values of modesty, etc. The long tunic in the medieval Roman empire was called probably a "hypokamision" or a "Dalmatica/Delmatikion" (the latter of which was originally a men's garment, which became a women's garment over the course of the migration era). There was also the "sphiktourion" which according to Dawson comes from Slavic "svyta" and probably refers to a tunic that opens down the front with buttons. However practicality was considered despite expectations of conservatism with medieval women - hence the short-sleeved dress known as a "Rouchon". Considerations of modesty would be traded off for practicality for the lower classes, but for the middle and upper classes they were more strictly confined by it, especially court women who would have specific codes of dress (as outlined in such works as the Book of Ceremonies, much like Chinese court dress).

Undertunics were worn - they were called "Kamisia" for men (hence the word Chemise, qamis, etc. in various languages) and an "esophorion" for women. So yes, multiple layers were used to keep warm.

Over the tunic, women typically wore a buttoned coat in Eastern European cultures (which were influenced heavily by the Roman Empire and the central Asian nomads) - by the height of the medieval era it is known as a "Diakoptos" or sometimes a "Kavadion" (which could refer to a Kaftan or a quilted gambeson).

Sources:

• Dawson, "By the Emperor's Hand - Military Dress and Court Regalia in the Later Romano-Byzantine Empire"

• Dawson, "Propriety, Practicality, and Pleasure: the Parameter's of Women's Dress in Byzantium AD 1000-1200" in Byzantine Women: Varieties of Experience (Pages 41-75)

• D'Amato, "Roman Military Clothing (3) AD 400-640" (for the discussion on Pants, specifically, pages 18-19)

Hopefully someone else here may be able to expand more on Viking considerations of women's dress, which at least in the Kievan Rus were heavily influenced by the Medieval Roman Empire.

While /u/FlavivsAetivs's answer is descriptive of regions in the Byzantine Empire, your question is quite broad - the association of long skirts with women (and by inference, leg-revealing clothing with men) in Western culture is long-standing and complex, not simply the result of Eastern fashions transferring into Western fashion through the Near East. To be sure, we can trace certain garments (such as masculine leggings) to this cultural transmission, but the notion of respectable women, or women presuming to be respectable, wearing some form of long garment as a matter of course can be found in numerous places in the ancient world.

For instance, in Ancient Greece, it is difficult to even find images of women without long skirts. This terra cotta lekythos from 6th century Archaic Greece depicts women at work on textile production, traditionally their realm: spinning thread, weaving on a warp-weighted loom, and folding the finished eima (length of cloth, which would be draped and pinned on the body to become clothing). They are all wearing patterned wool or linen, folded into peploi by turning the top edge down, pinning the folded edge over each shoulder, and fastening around the waist with a belt of some kind. This was the standard outfit worn by Greek women until the late Classical period, when it was displaced by the chiton: this was typically made from a linen eima much wider than that used for the peplos, almost two of the wearer's armspans wide, pinned over each arm with multiple brooches and belted at the waist. You can see a woman's chiton represented on this Classical statue.

Likewise, in Ancient Egypt it was extremely common for non-eroticized works of art depicting women to show them in a long skirt (as in this Middle Egyptian statuette from ca. 1980 BCE, or this figurine of a seated woman from the Late Old Kingdom, in the third millennium BCE), most likely representing a social norm. This is especially noticeable when the depiction of the woman is alongside a depiction of a man, as in the funerary stela of the Royal Sealer Indi and his wife, the Priestess of Hathor Mutmuti of Thinis, ca. 2100 BCE, since male figures are generally shown in short kilts.

Now, I don't mean to suggest that clothing traditions of the Ancient Near East were directly influencing those of Europe centuries later. Despite the ever-popular idea of "Western civilization" being descended in a direct line from "great civilizations" of the Mediterranean, this is not really the case. But my point here is that there does not appear to be a single point of entry for the concept - it was a long-standing tradition of indeterminate origin. And it is also attested early in Europe, as you can see in my answers to two earlier questions:

What (specifics) do we know about clothing of Northern/Central European men during the late Bronze- / early Iron-age? (I describe women's clothing in my follow-up answer)

Arts, Crafts, and Clothes of a 5th/6th century Saxon?

The cultural expectation was huge and well-established by the Middle Ages.

Was it more practical for carrying items

There are images of women in the Middle Ages using their skirts to carry items, but no, their ability to be flipped up into baskets does not appear to have been much of a factor in their extreme commonness.

was it actually warmer to wear layers of skirts (though that seems cumbersome)

Technically, women did not wear layers of skirts until the Early Modern Era. As described in the Saxon answer, women wore a linen underlayer (protecting the skin from wool and the wool from body oils), a sleeved gown, and a sleeveless peplos gown; on top of that, they could wear cloaks of varying lengths and thickness. Skirts are/can be warmer than people think, but it's also unlikely that they were deliberately worn by women instead of leggings because of length.

The thing about skirts is that they're the simplest garment to make. In the first two cultures I described - Greece and Egypt - men were also wearing non-bifurcated garments, and for much of the Middle Ages long tunics and gowns could be and were worn by men. It's not exactly that women were expected to wear skirts, as it was that when uncovered leggings and trousers started to be worn in Europe, they were restricted to men.