From what I was originally taught, "anthropomorphic" simply means that something non-human is being treated as human. So this could be said for any animals with human-like qualities, other living things (plants, fungi) that happen to have human-like qualities or even inanimate objects that happen to have been given human-like qualities (e.g. things like Thomas the Tank Engine).

So in MLP specifically, I would definitely say that the ponies themselves are anthropomorphic, because, even though they physically move around like real equines (walking on all fours, even picking things up using their mouths, etc.) they do have human-style personalities, emotions and expressions.

That said, there are some animal characters in MLP that are purely animal-like and I wouldn't consider them anthropomorphic! But when it comes to the ponies, then yes. :)

Great question btw!