[Kutara]

The following will hopefully be a helpful explanation of Dothraki culture, for those who wish to interact with them or perhaps play one in the future.  This isn't everything, yet; I will be adding on gradually as I get it typed.

Appearance
Physical Appearance
Dothraki generally have darker, copper-colored skin, and are lithe and muscular by virtue of their lifestyle.  Their eyes are dark brown or black, as is their hair, which warriors wear braided and decorated with small trinkets (arrowheads, bits of armor) to represent their victories.  Conversely, if a warrior is defeated in battle, their braid is cut so that the world may see their shame.  Among khalasars with a history of interbreeding with outsiders, variants in physical appearance are present, but uncommon.
Despite their savage appearance, the Dothraki are a clean people, bathing meticulously and treating their hair with scented oils.  If water for bathing is unavailable, they have been known to scrub themselves with clean sand.
Clothing
Leather tends to be the material of choice for Dothraki, though they are also known to weave cloth from horse hair, or even the grasses of their homeland.  Trade (or more likely pillage) with other peoples has brought more traditional clothing into the khalasar, though generally only as minor accessories.  The Dothraki have very little concept of modesty, and man and woman alike can be found in various degrees of nudity as the need or want arises.  Even fully clothed, they tend to favor looser, less restrictive clothing, except for the thick leather armor they wear into battle.

Culture & Customs
Horses
It should come as no surprise to any who have come into contact with them, that the horse is central to Dothraki life and death.  Even their name for themselves, "Dothraki," translates to "Those Who Ride."  Riding a horse is the most basic marker of social status: boys learn to shoot a bow from horseback when they are only four, and pregnant women are expected to ride up until the point of childbirth.  According to tradition, a khal who cannot ride, cannot rule, and will find himself quickly replaced.
Horses also provide their primary source of sustenance, and it is believed that consuming horseflesh will grant speed and strength.  This belief has translated to an aversion to other livestock, so that the average Dothraki believes eating beef or pork will make the consumer slow or dull-witted.  However, the bounty of wildlife in this new world has given them other options, and the Dothraki meal will often include venison or goat alongside horse.
The strength of a khalasar resides in its horses.  As such, the herds are fiercely defended from outside threats.  When in camp, the herd is cared for by slaves and adolescents, in addition to any warriors without a dedicated task.  While each warrior has their own particular horse, there are a number of others, unclaimed and generally regarded as common property.  Dothraki do not name their horses, though they may refer to them by their color, and have a great many terms to refer to different colorations, breeds, gender, and age.
Social Order
Dothraki travel in nomadic groups called khalasar.  In their homeland, many khalasars roamed the great grassy plains; however, in this world they have condensed into a single group.  The individual khalasars do not have names, but rather are referred to by their chieftain, or khal.  The khal surrounds himself with several kos: generals, commonly called blood-riders, whose bond runs deeper than friendship or brotherhood.  Tradition states that should a khal die, his bloodriders die with him, though this is not always observed.
There are two distinct types of healer found within the khalasar.  Koalakheesi are female healers, generally barren women, who heal with herbs and magic.  Koalak are male, generally eunuch slaves, who heal with knives, needles, and fire.  In the harsh life upon the plain, both are crucial, and highly respected.
Traditionally, men enjoy greater social status than women, and warriors have the greatest status of all.  However, with their numbers greatly reduced, the Cuiviénen khalasar has been forced to adapt.  Both men and women are welcome and encouraged to serve as warriors, but this is not their only role.  Every member of the khalasar, from the lowest slave to the khal himself, are expected to sustain the clan's survival, either by hunting and preparing food, providing weaponry, or performing other tasks required in their daily life.

[Kutara]

Culture & Customs, cont.
Religion
While the Dothraki revere a number of supernatural beings or spirits, it would be inaccurate to call them polytheistic.  They are more henotheistic in their beliefs: while they acknowledge the existence of other gods, who may claim power in certain locations, they worship only a single deity: Vezhok, the Great Stallion.  He gallops across the Night Lands, with the stars as his fiery khalasar.  It is believed that when a Dothraki dies, their soul will rise to the Night Lands and ride alongside the Great Stallion, and those who burned brighter in life will burn brighter in the night sky.  Because of this belief, the Dothraki burn their dead, allowing their ashes to rise to the heavens.  Conversely, to allow a body to rot and return to the earth is seen as a terrible dishonor.
While not gods in the same sense as the Great Stallion, Dothraki also worship and seek omens from the Sun, the Moon, and the Earth.  The Sun is believed to have been the greatest warrior the Dothraki have ever seen, so fierce in battle that his star burns brightest of all, with such ferocity that he serves as the Great Stallion's lone vanguard.  His wife the Moon travels with the khalasar, her light gentler than that of her husband, but no less a beacon to others.  The Earth, it is said, is the Mother from whence all life came, and is revered as such.  The Dothraki do not build, do not plow, because to do so would be to scar the face of the Earth Mother.  As a result, many victims of Dothraki conquest have had their walls torn down and fields laid bare, so that the Earth Mother may reclaim her land.
The closest thing to a priesthood the Dothraki possess are the dosh khaleen, a council of wise women who hold great respect among the khalasar.  They conduct religious rituals, interpret all manner of omens, and are thought to possess great powers of prophecy.  Bordering on the arcane, their ways are mysterious even to other Dothraki, but their wisdom is absolute.  Blood magic, on the other hand, is strictly forbidden among the Dothraki, and practicioners of such dark arts (maegi) are viewed with distrust if not outright hatred.

Music & Art
Life on the Dothraki Sea can be a harsh existence, but it is not devoid of joy.  The khalasar seems to operate to the ubiquitous beat of rawhide drums, from the joyful cadence of the children's drums, to the thunderous roar of the khal sado (khal's drum).  The wooden frame allows for ease of transport, and is usually crafted from pillaged barrels and crates.  Every member of the khalasar - from the youngest child to the most wizened crone - play drums, and will generally do so if given the opportunity.
More skilled Dothraki musicians will play flutes of various size and pitch.  While wooden flutes are preferred for their richer tone, suitable material is often scarce on the plains.  Instead, the long bones of horses are boiled to remove the marrow and used instead.  However, as trees are in much greater supply in Cuiviénen, this trend seems to be shifting once more.
Perhaps the most intrinsically Dothraki instrument, however, is the morinkhor, or horsehead fiddle.  Like so many aspects of their culture, its deceptively simple appearance belies its great depth and complexity.  The morinkhor is a string instrument with only two strings, made of horsehair and strung along a wooden neck, usually with a horse head carved upon it (giving it its common name).  By manipulating the tension of the strings and bow, the player is capable of achieving different notes, and can even mimic human speech and animal calls.
As the Dothraki are a culture with an oral history, song and music play a vital role in preserving their history and lore.  Song, especially, is used to tell the stories of their ancestors even if the original khalasar dissolves.  In addition to traditional singing, the Dothraki developed a deep, resonant technique that carries great distances in their native lands.
Due to their nomadic lifestyle, any art the Dothraki possess must be easily transported, if not worn upon their person.  Skilled artisans will often engrave or carve designs upon even the most practical belongings, transforming them and - in some instances - evoking protective entities over the item and its owner.  While leather is their clothing of choice, the Dothraki will often embellish their clothing with decorative embroidery, and have been known to sport truly extravagant designs when attempting to display their power.  Warriors wear trinkets woven into their braids to commemorate particular victories.  While many of these trinkets are trophies from the battlefield, some are intricately carved pieces of metal, bone, or wood, created either as a gift or as tribute to the warrior in question.