Short of just bombing the ever-loving fuck out of the whole region (and surrounding regions, if the fan-made expanded universe is brought into the question) we would have a hell of a fight on our hands. Earth ponies that can liquify our bones with a kick, flyers that can reach mach 5, and unicorns that can levitate our guns right out of our hands and turn them around on us. And that's before we get to the super-powered alicorns, Celestia and Luna. Celestia controls the sun, and Luna has just as much power. We'd be screwed.
Check out this Starscream vs Rainbow Dash Death Battle [http://www.youtube.com/watch?v=8er83h9Bbn8]. Tell me how eager you would be to fight THAT in conventional warfare.
Such a wildly unpopular war - because let's face it, there is no reason whatsoever to invade a land as undeniably peaceful as Equestria - would land our governments in severe trouble. One picture of a crying Fluttershy would send the masses into an outrage the likes of which we never thought possible. If our leaders don't turn back then, we'll just outright revolt and pull our troops out that way.
And personally, as an Army soldier, I would refuse to fight. Court martial my ass all you want, I'm not going to have pony blood on my hands. Hell, I think I'd sabotage whatever I can - safely, of course, because I don't want my buddies hurt, either - in order to cut down on the warfare.
Bottom line: Don't mess with the ponies. EVERYBODY loses when you mess with ponies.