Mounted infantry have been a part of Equestria's army for generations. While ponies themselves can travel great distances on hooves, mounts give them greater speed advantages and other capabilities that aren't wouldn't come up nearly as much with regular pony infantry.

Gallimimus

Gallimimus riders are the most frequently used mounted units seen in the Equestrian army. They perform a number of roles for the army. Given their incredible bouts of speed and maneuverability, they are often used as scout units. Being able to quickly view their opponents and running away before they are spotted. Gallimimus are usually lightly armored, so as to not cut down on their speed. This of course does make them vulnerable in close quarter combat, but given their powerful legs that can break bones and claws that can gut a diamond dog quite easily, they can still hold their own.

While mostly used as scouts, they do serve a purpose on the battlefield. They harass and charge into weakpoints in the enemy army, bleeding the enemy dry as their riders cut, stab, or shoot anything that comes close. The Canterlot Mimus Brigade, the most famous Gallimimus brigade in the country, has proved time and time again that they can turn the tide of battle. Another nifty feature that some commanders use them for is quick time infantry transports. Moving a unit of musketeers/crossbow ponies into positions swiftly and with deadly consequences for the enemy.

Each Gallimimus brigade breeds their animals to have different colors, distingishing them from their comrades. While Mimus from Canterlot have golden feathers overall in honor of Celestia herself, some such as Goldshire raise blue and red breeds.

Ungul - hadrosaurs

Unguls are species of hadrosaurs that have adopted more 'equine' traits over millions of years. Some ponies have jokingly referred to them as 'lost cousins'. Joking aside, they are a valuable part of military and civilian life. There are a number of Ungul species, ranging in sizes. Medium sized Unguls are usually used by civilian transports in cities and towns, pulling carts behind them to their destinations. When trains aren't available for military use, Unguls fulfill this role there as well. Some of the larger ones help move large military pieces of equipment in less then ideal terrain as their strength and endurance is a boon in such environments.

Unguls are also used in war chariots. Their strength and size allows them to run over and crush many opponents as well as crash into them with their strong skulls and horns. Unguls can survive collisions that would even kill an earth pony. While normally placid, they can be a danger when spooked and terrifying to face by yourself on the battlefield.

The largest of them all are used as mobile bases/roosts, with small cannons and infantry place themselves on top of sturdy wooden platforms to fire down on enemies as the beast lumbers through opposing lines. They can help break holes in enemy encampments and walls. While they do offer a large target to the enemy, this of course gives Equestria's soldiers some breathing space in many cases and the ability to overwhelm their opponents.

Wyvern

Having first domesticated by the pegasi before the unification, Wyvern are primarily used by the high fliers themselves. While some have pondered why a flying race predominately uses a flying mount, it's quite clear that pegasi know what they are doing. Given that wyverns aren't sapient, they need a handler to keep an eye on them. In recent centuries, other races of ponies have taken to becoming wyvern riders as well though it's still primarily pegasus riders. In combat, their handlers steer them where they need to go. Wyverns can fly swiftly, with some breeds even outpacing pegasi.

Strafing enemy lines, they can quickly cut holes in the opponents ranks with their claws, teeth, and more importantly fire. However, they are also used in conjuncture with the Wonderbolts and other flying units as sort of bruisers in aerial combat. Given their temperament, Equestria is one of the few nations in the world who have Wyvern riders used regularly in their army. This gives them an advantage in many combat cases. Once tamed, they are fiercely loyal to their riders and units, unwilling to abandon them if ordered to retreat.

Their thick hides, already impervious to light arms, it usually covered in enchanted armor. This gives them added defenses and survive-ability, allowing them to take out key units in an army with the added bonus of being able to retreat with little to no damage taken.

5429951 Quick question, were did the Unguls come from? How did they survive the mass extinction that wiped out the rest of the dinosaurs?

5430044 Equis is much larger then Earth and some species were able to survive the mass extinction on more remote areas of the planet. However, Equestria didn't have any Unguls or many other creatures native to the region until Discord's era where he mashed up the continents and brought back every single species to have existed, for the fun of it.

5430116 Thank you for the answer. And I assume this is the same for the Gallimimus?

5430117 Yep, well they were extinct actually until Discord. So yeah.
{I really need to do blogs on the overall history of Equestria. A part of me ponders doing something like the History of Equestria videos.}

5430125 That sounds like a great idea

5429951 I am freaked out by quadrupedal ponies riding the bipedal gallimimus, for some reason. It's just not natural!

5430766 Said Quadropeds can maintain bipedal postures for quite some time and have flexibility that normal ponies lack.
Also, magic~

5430795 I recognize all that, it still freaks me out! If I was in the invading human armies and I saw some pony sitting up on his back hooves, riding at me with a giant bird loping forward on two legs with a hunched posture so his rider can stay on, I'd probably just stand there gawping until I was gutted like a fish.

5430912 One more tally of the enemies of Equestria!

5430912 Also, Gallimimus is a dino. While birds are descended from dinos and......... Oops, went into nerd mode. I have a passion for extinct animals.

5430928 If it has lots of feathers, it is a bird. It may also be a dino, but I count it as a bird.

5430928 - You an me both. Dinos rule!