Since one can make posts public, is it possible to search for say, all users who mentioned "Ponies" in their posts? Specifically I am looking for people who have posts pertaining to "My Little Pony"
You can use the "Search" box in Google Plus. It's just to the right of the Stream/Photos/Circles/etc. bar.
You can further refine the search to just posts (in your circles and public posts) https://plus.google.com/s/Ponies/posts
Don't forget to use "Best of" / "Most recent" per your needs.