'pulling faces' is a term humans apply to the way a horse communicates using his head, ears, eyes and mouth.
It could be applied to a negative expression; such as teeth barred and ears set back. it depends on it's context in an advert. So if the advert states 'lovely horse - doesn't pull faces' it could mean the horse has never been seen to put it's ears back or show it's teeth.
Horses use their body to communicate with each other and us and I do not think there is a horse which doesn't pull a face at one time or another unless it is a stuffed toy
My big lad pulls some amazing faces, he can look really horrible sometimes, especially when he's got a feed, to the uninitiated he can look really threatening, but that's all they are, just faces. I like the fact the ad you've seen was honest about the horse making faces.