Through The Next Generation and Deep Space Nine, the majority of the Ferengi we see a wearing a headdress on the back of the head.
Quark though, on Deep Space Nine, does not ever seem to wear one, even though his brother, Rom, and his nephew, Nog, do wear them.
Is there ever a reason given for why Quark does not wear this headdress?
Starting with Quark and the launch of DS9, Ferengi characters started showing up sans headdress in both DS9 and TNG. Other than the noted exceptions of Rom and Nog, it seems only speaking Ferengi do not wear headdresses. This is probably to cover up prosthesis seams easier than making a full upper torso piece.
As with many canon uniform/outfit questions we can only speculate since it is not directly mentioned in the shows and may be an artifact of current fashion without greater symbolism. But looking at the characters who wear or don't wear the headdress we can infer their symbolism and meaning. All Ferengi that we encounter without the headdress are all known as businessmen, are successful financially, or otherwise dictating their own path (in the case of Dr. Reyga). And those who wear them are either adolescents or those who are not entrepreneurs.
Also, headdresses seem to be somehow related to the earlobe, usually continuing from the top of one lobe to the other. This could be related to the cultural superstition of earlobe's relationship to business acumen, as seen in the of repeated phrase "the lobes for business".
Possibly they originally were created as some sort of hat (considering their home climate) that emphasized the earlobes because of the superstition tying them to success. But as time went on it was considered a sign of small lobes to wear the hat, so it eventually shrunk to the tasteful back band headdress. Quark, Brunt, Zek, and others don't wear them because they are confident in their lobes and don't need any adornment to emphasize them. A parallel could be drawn to the human top hat or fedora, originally used to indicate status, but has fallen out of favor and seen as garish or humorous.
And Moogie, well she is female, no headdress for her. :)
Notable examples of Ferengi along with their headdresses:
To add on to previous answers, Quark wasn't above wearing a headdress when it suited his purpose, such as in this scene from DS9 5x03 Looking for Par'Mach in All the Wrong Places, where he's wearing one (at least in part) to conceal a device that Worf is using to help Quark win a bat'leth duel.
For what it seems, the Ferengi caste system works as the following.
Male Ferengi WITHOUT a headdress is head of the entire family household (main household) and MAY be the oldest if he has the most money.
Male Ferengi who wear suits with tails and fancier decorated suits have high status, the longer the tails the more the status.
Suits lacking tails are of low status and is NOT head of the main household. If a male Ferengi is not married and the father is dead he has the care of the entire household and his status is shown by the cut of his clothing.
If the brother or lower caste brother becomes married he is still not head of the family household unless he can financially support everyone in the main household and his household too.
And with the caste system comes decor--the fancier the suit/dress, the longer the tail the higher the status of the male Ferengi.
So basically, no headdress, long suit tail, and fancier decor marks a high caste and the head male Ferengi of the main household. With a headdress, no suit tail, and a conservative decor the lower the caste and is not the head of the main household.
I brought up this question with my husband, hence the search that landed me here. While I have no clue why some do and some don't he suggested that rather than wealth or success it has to do with family position. Quark is a first born son so doesn't wear the headskirt. Women were condemed for wearing clothing, could it be that a second born son would be condemed for being seen without the headskirt?
There is one possibility I haven't seen covered yet and that is that the head dress may be something in-between stylish and practical. Maybe it's the Klingon in me but looking at the basic design, the fact we see it a fair if not in every situation in which one is serving aboard a Star Ship it may be the head dress is actually a form of cranium or neck armor meant to protect the head or neck from attack. As the Ferengie became less militaristic it was something used more as a comfort in the same way that one might wear a belt with pants that fit after years of wearing loose pants. Considering the design of the Ferengie head protection of the lower back part of the neck from attack would make sense.
Perhaps a headdress is considered formal attire, like a tuxedo in human culture. If this is the case, it explains why Ferengi in the more strict environment of a starship - both Ferengi and Starfleet - always wear them. Similarly, the headdress wearing Ferengi at Quark's may simply be dressing to impress, where as Quark - who is the face of the business - does not wear one as he wishes to appear like a relaxed host. This makes Nog's wearing of a headdress while in Starfleet similar to how Worf wears a sash displaying his family crest, which explains why he was allowed to wear it even though it would seem to defy the standard Starfleet dress code - they would be less likely to allow this infraction if the headdress were simply an item fashion.
Grand Nagus Zek however, does not wear a headdress - this is perhaps because his staff confers his status more effectively than formal attire could. Brunt also goes without a headdress, this is perhaps done as an insultive gesture towards Quark and other Ferengi that his FCA duties have him deal with - he refuses to dignify these people by putting on formal attire. Dr Reyga does not wear a headdress as he seems to object to many of the conventions of his culture. Pel's lack of headdress might be due to her own ignorance, the patriarchal Ferengi society is unlikely to teach a female correct etiquette, this was probably only tolerated as Quark was infatuated with her.
Nobody mentions that in DS9:7x10 "It's Only A Paper Moon," Nog is wearing the head skirt while in uniform and while he's depressed on his medical leave. However, once he moves into the holosuite and starts enhancing the success of Vic's business, he dresses in "upper-class" attire for Earth in the 1960s and does not wear the headgear. Then when he returns to the uniform, so too does the headdress.
IMHO the insurance of Quark wearing one to disguise the mimic equipment to win the bat'leth fight in DS9:5x03 should be ignored for these purposes, as it is both the singular instance odd Quark being seen wearing one, and is specifically being worn to conceal the deceit. Had he not needed to cover the device he would not have worn one, sorted by the lack of headdress when he appeared before the Klingon high council when first meeting Grilka in "The House of Quark (DS9:3X03)."
I think the on screen evidence supports the lack of headdress being a symbol of entrepreneurial status (females notwithstanding, as they are denied the wearing of clothes for most of the timeline). No matter how "successful" your business is, if you're a business owner you can go without the headgear (i.e. Quark lacking his own despite several instances in DS9 of the bar being on the verge of closing and Quarrel nearly bankrupt). It might also hold that it is a matter of military custom or uniform regulation that Ferengi wear the headdress, which would carry over to Starfleet based on Nog's recommendations for customs and traditions - Starfleet likely did not have a relation governing Ferengi culture as Nog was the first in Starfleet. This would explain why civilian business owners would forgo the head skirt while subordinates would wear them, while even high ranking members of Ferengi military or paramilitary organizations and Starfleet would still wear them. Just a thought.
I just want to point out that Star Trek is exceptionally well known for inconsistencies. In this particular case, it should be noted that TNG first introduced the Ferengi as a pseudo-villainous culture with minimal appearances, thus it can be assumed that the the cultural background was not fully fleshed out at the time (aside from the the ideas of a predominantly capitalist society and basic costuming features such as the headdress). Also in terms of status and rank with regards to the headdress, DS9 is the only reasonable source of accurate information, in which case I agree that the headdress is representative of status and most likely wealth. The following series of Voyager distinctly portrays a facsimile of Starfleet HQ created by species 8472 (something around 5 or 6 years after DS9, I don't know the exact episode number) with an abundance of Ferengi SF academy students, all wearing headdresses. This either implies an acceptance of Ferengi into the federation during that time, or a misunderstanding by species 8472 about the federation and its members (since there would not have been any Ferengi on Voyager as Nog was the first to join Starfleet after voyager left DS9, and when compared to the Bajoran acceptance process and the exceptionally apparent conflicts of the Ferengi rules of acquisition with Federation guidelines would have taken more than 6 years to to gain Federation membership)
It should be noted that several races have been significantly revised since their first introduction (such as the Klingon) since their first introduction in TOS, and as a result, the franchise has suffered by focusing on trying to correct these inconsistencies (Star Trek: Enterprise trying to explain the transition of very human-looking Klingon of TOS to the the makeup costumes of TNG ended up as something of a train-wreck of bad storytelling and even worse acting)
Has anyone seen a Ferengi without the head skirt while working on a starship? Even the Daimon are seen wearing the affectation.
Now, presuming the previous conjecture that those Ferengi serving as subordinates in an institution wear the head skirt, this would seem to fit, however, Nog was seen wearing the head skirt throughout his youth before starting his career in Starfleet.
It could be that children are simply considered subordinate as a general rule, but we don't have reference for other Ferengi children to know and it could just as easily be that Nog was employed by his uncle in some capacity and therefore a subordinate within his business. The way that Ferengi regard business and income, it's not unlikely that Ferengi (male) children might enter into the workforce at a younger age.
Admittedly, this is just further conjecture but with so little concrete information, it's fun to throw ideas around.
Canon answer I believe the head dress has to do with the near constant rain on Frenginar. This became a part of their culture over time and people adhered to it even when not in rainy climates where the head dress was useless. I would say this is similar to how United States males wore hats when outside all the way up to 1960 whether not their vocation or stature called for it. In fact a man who didn't wear a hat was often seen as poor. What changed you ask? John F Kennedy was elected president and he had a personal preference against hats. Almost over night the practice of business men and others who didn't need to wear hats for work disappeared (not completely) . Quark is an individual with a preference same as Nog or Brunt. I know hat's in the United States dying out is an oversimplification and there will always be outliers and situations to wear hats. I myself am not a hat person but I'm going to a baseball game where I enjoy wearing a hat. Infact I'm wearing my Deepspace Niner replica hat!
Out of Canon answer
Make up chair hours and money saved, sadly 21 century humans are a cross between Frengi and Cardasians.
In my own head cannon, the Ferengi head skirt is a combination of formal atire and vestigial armor. Compare Quark to Humphrey Bogart in Casablanca (and many other "bar" movies/TV shows). The employees are in formal wear, the boss is in a smoking jacket or other more relaxed atire. Then, think of the Klingon uniform with its spine armor; not exactly practical in a phaser fight, but worn as part of the traditional formal military atire.
The only time in cannon where Quark wears the head skirt is when he's in a bat'leth duel. Looking at the photo above, the skirt is the same color as the klingon armor; so it's probably metalic actual armor. All other instances of the head skirt I can recall have a more cloth-like appearance. It's possible that the back of the head is a Ferengi weak spot and the head skirt performs the same function as a human breast plate/body armor; protect the vunerable parts. I believe Quark planned to wear his culture's armor for additional protection along with the Klingon armor and Warf just leveraged that for the cheating device.
I suspect that it is a sign of endenturement, from what I understand of Ferengie business custom, when a ferengie has made enough profit to buy his debt to his family or other institutions, he is permitted to remove the headwear, hence the reason why "succesful" Ferengie do not wear them. Nog has no chance of profit working for starfleet and therefore is unable to buy his headwear off, the same with Rom who, on multiple occasions, has proven to not have the lobes for business. This also goes to show why all the staff and military also have them, as they do not earn enough money to be able to buy it off.
This is purely speculation on my part, but it is my theory.
