I imagine the training would be split into multiple groups depending on the pony's class (Unicorn, Pegasus, etc). Twilight showed off what Unicorns can do on the offensive in the finale, so I would include that with Trixie's experience. Regarding the other classes, I imagine that the Pegasus would be tacticians/commanders that would lead the Earth ponies into ground assaults. I suppose the Earth pony's arsenal would include ramming headgear and perhaps something like jousting spears.
Now, regarding Trixie's experience in this military, as a reader I would like to read about what prompted the creation of the military. Things such as the atmosphere of the training program and what these trainees will do after completing their training would be interesting to learn about as well. It would be very cool if this story evolves into a potential war between the ponies and Changelings after the events of "A Canterlot Wedding", not to mention you could throw in some tension between the ponies and the Griffions/Diamond Dogs, so you have a lot to work with.