I believe the Equestrian Royal Guard is but the "cavalry" component, kinda like the British Life Guards or Napoleon's Cuirassiers. However, I must assume it goes further than that.
If we base it on, say, the Napoleonic age (which kinda fits MLP, in a way), I would suppose their military should have the 3 components Blue mentioned.
A smart commander would place, by excellence, Earth ponies as Line infantry, Engineers or Sappers, due to their robust size and muscles, while keeping Unicorns as Light Infantry and Skirmishers/Rifles. Those who are fast enough would be placed, no matter their "tribe", in a "cavalry" division, which would charge with lances, swords, or simply sharpened horns.
Pegasi would form the aerial component, fighting in an early WW-1 style (a single pegasus would have a really hard time carrying a heavy bomb or weapon, kinda like old bombers).
The naval component would not be very different to that used in the Napoleonic Age.