A pig eyed horse is one that has disproportionately small eyes. It is generally considered a fault, both because it's viewed as unattractive and because it's associated with stubbornness or anxiety. This latter may have some truth to it - the smaller eye may result in less peripheral vision. For the most part, though, it's an aesthetic problem.
This chestnut horse has a pig eye, and the eyelid does not appear to open all of the way. Image source: Rachael C via Flickr.