Hygiene and regulation of appearances has been part of the military since at least the eighteenth century. I cannot speak for medieval and ancient times. I would argue that current grooming standards have at some degree pulled inspiration from past centuries and adapted to current necessities. Most of the armies in the eighteenth century had some form of queue, pigtail, clubbed hair, braided, or hair dressing of some sort, but also regulated other manners of grooming.
The queue remained in fashion for most of the armies until after the turn of the nineteenth century. However, in some periods of the eighteenth century armies issued orders for short hair. Now this did not meant the high and tight closely cropped hair of more twentieth century and on, but more of just a few inches in length. It would appear shaggy to our current standards. The thought of short hair being easier to maintain and more hygienic can be dated to the 1750s at least with Maurice de Saxe, a prominent military writer and commander.
I would rather have a soldier wear his hair short and furnished with a small wig...This wig will resemble the natural head of hair so well, as to render it almost impossible to distinguish the difference
In the Field, the hair is a filthy ornament for a soldier, and after once the rainy season has set in, his head can hardly ever dry [Maurice de Saxe, Mes Reveries, 1759]
However not all armies followed this. Wigs could be expensive to procure for every soldier and maintain on a constant basis. When armies did call for men to have long hair and dressed into queues, they preferred to use the men's natural hair and if a man could not meet the standard, officers often bought false queues for them to wear until they did meet the standard or remained with it if the soldier had a lack of hair for it. In 1776, General Howe gave out orders to cut the men's hair short for ease of maintenance and hygiene. The American army followed shortly afterwards with orders going out in Pennsylvania regiments to cut the hairs short. Something like this had been done earlier in 1758 with Lord George Howe ordering the men of the 55th regiment to cut their hair, he even cut his own hair short, along with uniform changes.
Now head hair was not the only hair part of the grooming standards. Armies regulated facial hair equally if not more so than head hair. Most armies required men to shave at least every three days, and for those that had any amount of growth from a lack of a shaving routine to immediately remedy their fallen standards. Review days, inspection, or threat of parade would increase the scrutiny of officers and non-commissioned officers on the appearance of the men. It was not uncommon for soldiers who had formerly been employed as barbers to find themselves in the same occupation in the army. They could actually get extra pay from it.
The only exception of clean shaven soldiers came from the grenadiers of various armies or Germanic soldiers. The fashion for mustaches among these units or armies came from an inspiration of Turkish or Balkan troops. These grenadiers imitated looks of the Ottoman Empire's Janissaries with tall caps, grenades, and the mustache. David Morier painted some grenadiers in the first half of the eighteenth century and quite a few had mustaches. The American and British army remained consistent with the clean shaven rule among regular infantry and grenadiers.
Armies also enforced a clean appearance for the soldiers. Laundering clothes became a norm for soldiers. Any mud, dirt, or other stain on their uniform would have to be removed by next inspection. Maintenance of uniform included patching and stitching any tears in uniforms, missing buttons, adjusting the fit of the uniform. Flour and oats could be used to remove stains and bring back some whiteness from older wool. Soldiers could get penalized for uniform infractions. I do not expect that these soldiers had a Sergeant Major Sixta on the maintenance of uniforms and adherence to grooming standards, but the soldiers had rules and expectations to follow.
My knowledge ends at the end of they century, but I know most armies enforced a shortened hair regulation after 1800, and in some cases remained clean shaved. I hope some other historians can chime in on 1830s and on, especially Crimean war, American Civil War, and on with some of the most glorious beards photographed.
It's difficult to make any particular arguments about the fdeveolpment of grooming standards in the US Army, because the nature of the politics surrounding armies meant that the United States has almost always gone to war with a force made up mostly of amateurs - the professional ranks were, prior to the Second World War, very small. It means that getting a clear picture of the type of grooming standards that may have applied to regulars in long-term service might get confused when we look at pictures of the amateur militia or volunteer forces that served alongside them; militias operate under their own state-defined regulations, and while volunteers in wars like the US Civil War were technically under the same code of conduct and regulation as the professional regulars, the standards were often relaxed or considered secondary to other needs.
However, we can at least trace a little bit about this:
...[officers] inspect into the dress of their men; see that their clothes are whole and put on properly; their hands and faces washed clean; their hair combed; their accoutrements properly fixed
eventually turned into this:
3–2. Hair and fingernail standards and grooming policies
Note. This paragraph is punitive with regard to Soldiers. Violation by Soldiers may result in adverse administrative action and/or charges under the provisions of the UCMJ.
a. Hair. (1) General. The requirement for hair grooming standards is necessary to maintain uniformity within a military population. Many hairstyles are acceptable, as long as they are neat and conservative. It is the responsibility of leaders at all levels to exercise good judgment when enforcing Army policy. All Soldiers will comply with hair, fingernail, and grooming policies while in any military uniform, or in civilian clothes on duty.
As previously mentioned, the US Army - or rather, the US State - maintained an enthusiastically amateur armed force, composed mostly of militia and of small number of regulars. Prior to the US Civil War it averaged fewer than 10,000 soldiers in uniform, and was expanded only in times of international tension or imminent war. Each state's militia was able to enforce its own standards and regulations, and often did. So while the regular forces started using Baron von Steuben's "Blue Book" for its infantry regulations, and eventually switched it out for what was essentially a translation of the army of the French Revolution's drill book, militia forces might have kept hold of Steuben, used a French or a German or a British manual, or even had a particularly motivated officer write their own. Among those, there might be variant standards for grooming, but let's focus on the standard manuals for now.
Steuben's book is quoted above, and says almost nothing about the specific grooming that was considered standard. However, not having specific prescriptions for grooming doesn't necessarily mean that there wasn't some enforced standard. Armies are as driven by culture and fashion as any other organization, and more than many; it would be very likely that individual companies or regiments might have some preferred fashion or specific type of haircut. Some older regulations deal with wigs and clubbed or pigtailed hair not necessarily because they were enforced by regs, but because men had them anyway and in order to make a neat, military appearance, some prescription, however vague, was necessary.
We can see that same remains true in the US forces up to the Civil War and after. The regulations of 1861 say:
(100.) Where conveniences for bathing are to be had, the men should bathe once or twice a week. The feet to be washed at least twice a week. The hair kept short, and beard neatly trimmed.
Note that the hair, here, is placed in implicit connection with grooming and cleanliness.
By 1889, the standards had evolved to:
(262.) The utmost attention will be paid by company commanders to the cleanliness of their men, and to the police of barracks or tents. Where conveniences are to be had, the men will be required to bathe once or twice a week. The hair will be kept short, and the beard neatly trimmed. Dirty clothes will be kept in the barrack- bag. No article of any kind will be put under the bedding.
Can you guess what the 1918 regulations for the US Army said about hair?
The hair will be kept short and the beard neatly trimmed.
Note that, despite a lot of repetition from pop history and reenactors, there is nothing in here about grooming standards as they apply to wearing gas masks. Beards had fallen out of fashion by the early decades of the 20th century, and while we might be able to make a soft connection between trimmed, short mustaches instead of waxed handlebars and the necessity of gas mask use, we can't definitively prove anything - at least not from these particular manuals.
However again we should note that armies are subject to fashionable fads; in the period following the Civil War and the First World War, the Us Army engaged in mor ethan 200 battles against Native Americans in the American West, and many more in the Philippines, Cuba, and elsewhere. Looking at photos of those various campaigns, you'll see a huge variety of facial hair styles and hair fashions, but generally when you're looking at regular, professional soldiers the fashion was short, neat hair and a handlebar mustache. Sometimes you'll see someone with a more luscious mane and sideburns, and clean-shaven faces were at least as popular as mustaches - we only really see beards and other unusual haircuts when regulars are engaged with civilians, scouts, contractors, militias, posses, or other semi-professional or contracted troops.
We see a change in this more or less unchanged standard by around the Second World War, when the 1940 Soldier's Handbook said:
All soldiers are required to have a short haircut known as a "military" haircut. This is done for sanitary reasons and to secure uniformity.
This is a pretty significant departure from the usual, somewhat laissez-faire approach. And note that the reasons given are due to cleanliness and uniformity, more than anything else. As the decades continue, more and more specific guidelines are written out, until you get to the modern day's exceedingly long list of regulations.
The modern guide even comes out and says that "many hairstyles are accepted" meaning that the "jarhead" look mentioned in your question isn't necessarily enforced by regulations, but rather encouraged by a shared culture, such as every army in every period in history. There are, of course, practical reasons that this might be popular, but in essence it seems as if it was as much a signal of peerage and group-belonging than any particular enforcement of regulations. And when it comes to it, there are some instances in which group bonding, peer pressure, or other cultural pressures might make the difference between "enforced" and "voluntary" choices moot: armies being no exception.
Hope this helps!
1812 Manual "Regulations for the field exercise, manœuvres, and conduct of the infantry of the United States" available here
Modern US Army regs, here