The way in which hair is worn often symbolizes the social group to which one belongs. As fashions change, these associations can come and go; therefore, it is best to determine the fashion of a time rather than the past thousand years. Hair styles change more rapidly than that, generally, over the course of decades or a few hundred years. However, a more insular society might retain them longer. We often mock both current and previous styles as embarrassing as a way of distancing ourselves from the period or the perceived values of that group.
An association may be all that’s needed to establish a hairstyle. In the 16th through 19th centuries, many men wore white, powdered periwigs. This spread from France to other parts of Europe because Louis XIII covered his baldness this way; the wigs became associated with power and eventually became quite elaborate until a taxation on the powder set in motion their demise. Women didn’t typically use them unless they, too, had lost their hair, but men had their heads shaved so they could wear these wigs, which were considered cleaner than their own hair due to sanitary conditions at the time. In our invented world, we can ditch the powder, use something besides white, or make them shorter and more functional. We can also make wigs less or more ridiculous, but remember that we need to describe it to a reader unless we’re in another medium.
In the U.S., long hair on men was once considered feminine and counterculture. In Game of Thrones, a Dothraki warrior with a long ponytail signified how long it had been since he’d known defeat. Samurai wore the chonmage style to help keep their helmets on during battle. This functional origin remained while also becoming a status issue. What country (and culture) do you associate dreadlocks with?
As this is not a treatise on hair styles, it’s recommended to perform an internet search and make a note of what’s been done or invent something yourself. Decide which group uses each style. In our world, we don’t need to define the source of one and can assign them without a rationale, though if one occurs to us, we can note it. People generally accept that a style belongs to a group without questioning it; so will our audience, simply because we said so. If we want a species to have a style, choose one that has variations, such as most elves wearing periwigs but one culture going short, another long, and both use white while a different one uses green, for example. This gets us unity but avoids a species monoculture.
While hair color is not typically cultural, it can be. East Asians so often have black or dark brown hair that we can be surprised when someone’s is different. Denmark, Norway, and Sweden have long been associated with blonde hair and blue eyes. Punk musicians have often dyed their hair colors that don’t naturally occur.
Facial hair can also be cultural. A long beard may symbolize virility, strength, manliness, or health. A shaggy one can suggest someone is wild and crazy, while a neatly groomed one suggests refinement and civilization. We once again want to decide what’s expected based on cultural vision: do we foresee people being meticulous or not?