(Note: the below follows own historical timeline which differs from later canon in some ways. Most importantly, the Royal Sisters came to power after deposing Discord, as seemed the case back in Season 2.)

Part 1 - Pre-Classical Era
It is not known for sure when the first true pony militaries emerged, save that it was before the earliest written records - over a millennium before the banishment of Nighmare Moon. Archaeologists can point to weapons and barding much older than that of course, and artistic depictions of their use, but are less able to pinpoint the stages at which defenders and raiders gave way to militias. Prehistoric folklore also offers few clues - it is agreed that the ponies needed no weapons in Dream Valley (while some stories blame the expulsion on fighting and quarrelling, this can be presumed to be unarmed), but little attention is given to how this changed on the outside save by the pegasi, who recount various clashes with griffons, dragons and other beasts of the skies.

With that in mind, it should be no surprise that pegasi cities formed the first real full-time militias - indeed, the word itself is a Pegas one - for defense against both such foes and each other. This was also around the point they began conquering ground towns, although scholars have not been able to agree on the cause-and-effect there - was that the goal all along, or just something to do with such a regular force when not under attack? In any case, such raids imposed an evolutionary pressure on earthpony militias, with only those tribes with effective ones remaining independent - especially when the unicorns got in on this "armed forces" game.

Eventually, the Great Invasion (by several griffon tribes with draconic backers) saw most of the pegasi cities unifying their command structure - a change which stuck after the war due first to wariness of a recurrence, and later due to a clever ploy where young pegasi of different cities were raised together. The society thus formed remains even to this day, when ponies are much more numerous, the largest army in our history.

It was the threat of such a force which inspired the unicorns to first seize control of the sun and moon, for they knew that even with their magic they could not hope to face the pegasi in war and emerge victorious. It was the subsequent inter-unicorn clashes for control of said bodies which saw their military skills develop, and of course Queen Majesty who organised the first effective unicorn army. How effective is a matter of debate - indeed, measuring it against the Pegasi Alliance is the biggest debate of Pre-Classical military historians, especially since the two clashed inconclusively on several occasions.

Comparatively, the earthpony militias are somewhat overlooked, perhaps because they remained a multitude of individual forces which would work together when necessary rather than even the semi-unified Unicorn Legions. Still, it would be best to remember that despite this, outside control of earthpony territory declined sharply as time went on rather than growing as some might expect.

Finally, besides such organised forces it should be noted that this era saw numerous mercenaries, both individual and in bands, who offered their services to cities, towns and individuals with a need. While most operated within their own tribe, many mixed bands (some even including non-ponies!) existed as well, offering all sides access to some amount of each other's abilities when necessary.

excellent world-building, I love stuff like this.

(Addendum - while armies and by default air forces were starting to develop by this time, no power in this era fielded what could be called a navy by modern standards. Ships were used for, well, shipping, and while the crews were often armed to fend off raiders and sea monsters they were not generally used in unison. The closest thing was Royal Legions commandeering merchant ships for transport on occasion.)

Part 2 - Classical Era

Ask the common pony, and you might get the impression that Equestria post-unification was a single fairly mixed state like it is today. Ask one who knows a bit of history, and they'll point out that in the early days the tribes still maintained self-governance, perhaps also mentioning the remnant states. And ask one who knows a lot of history, and you'll find it's more complicated than that - the initial merger left the tribes with plenty of independence, but there was also a fair bit of entanglement even below the level of the Triumvirate. And the military was one of the areas most affected by this.

Of course like every other aspect of society, the armed forces were spilt between those who migrated to the new land of Equestria and those who didn't. The Royal Legions held together better than most, while the Pegasi Airmy split surprisingly hard - the earthpony militias, of course, all followed their clans.

The actual split occurred largely without violence (in the hope of not further inciting the windigoes), with the various armies guarding the migrant populations from monsters and bandits. Once arrived, they maintained this role for a while. But a combination of griffin raids and it becoming clear the ponies left behind weren't just going to freeze over lead to a push for greater military coordination. Under the guidance of the Triumverate, senior ponies within the Royal Legion, Pegasi Airmy and the most prominent militias were united as the first Equestrian Joint Staff. While as in the civilian sector, each body retained it's own chain of command, the Joint Staff and their bureaucracy helped coordinate between them as necessary, as well as taking over the organisation of mixed-pony units (many staffed by former mercs).

So Classical Equestria in a way retained the armies of it's parent tribes (at least in part), while also making the first steps to integration. As with the state in general, said integration fluctuated, but ultimately grew over time - the idea of fully merging them was being strongly considered before Discord ended the Era in chaos no military could oppose. Equestria's first navy also arose in these years, to protect it's trade ships from pirates and privateers - as today, much of the crews were pegasi.

A word should probably also be spared for the militaries of the Remnant Tribes, which started as the leftovers of the original tribes's militaries but. through a mix of copying Equestrian advances and some innovations of their own, mostly became respectable enough forces over time. Their main enemies were each other and griffin raiders, but they did also clash with Equestria from time to time - initial results varied, but the larger, united state would always eventually bring enough forces to bear to stem any incursion.