It seems that while Equestria's government is ruled at the top as a monarchy/oligarchy by Princess Celestia (a pony with both a horn and wings) and Princess Luna (the same type of pony as Celestia). However, all the confirmed royalty are unicorns, pegasi, or both. In addition, the vast majority of the royal guards are also either unicorns or pegasi. It seems like the rulers of Equestria are not paragons of diversity, is there any indication that there are powerful earth ponies in the Equestria government?
Depends at what point you start calling it "government"; in the show I've never seen "royalty" represented as anything but a winged unicorn, but there's only the two princesses.
Assuming you don't mean strictly royalty, there's definitely Mayor Mare for a government figure:
Image from mlp.wikia.com Copyright by Hasbro
Additionally in the Gala episode there were several well-dressed Earth ponies in with the rest of them, showing Canterlot (I think) isn't Unicorn exlusive.
Earth ponies do possess abilities the other races lack, like the ability to grow food. They are also generally stronger. I believe an alicorn is all three races commbined, including the magic of a unicorn, wings of a pegasus, and brute strength/food growing power of an earth pony. So yes, I think earth ponies are represented in the government.