Pharfignewton is Pinky's horse girlfriend(who according to Rob Paulsen's podcast is a Clydesdale). She and Pinky have seemingly been in a long distance relationship throughout the series, as shown by the pictures of her Pinky has in the cage and for himself. Her voice has been provided by Frank Welker and Rob Paulsen.
As she only appears in person 2 times, once in Animaniacs and once in Wakko's Wish, we don't know too much about Pharfignewton's personality. What we do know is that she is madly in love with Pinky, even defying the odds and winning a horse race just so she could get Pinky off the ground. She appears to possibly be just as dumb as Pinky, but as she can't talk, it's not too clear.
Pharfignewton is a large, white horse. To get the idea of her size, it's shown that her snout is basically the size of Pinky's body. Her vacant blue eyes and large overbite are nearly identical to Pinky's, leading Brain to remark, "Heavens, they're multiplying."