I actually cannot say that I have met a horse whom I'd call ugly by facial characteristics. And I have met many and various. Why, my own gelding was hammer headed and with particularly small eyes when I bought him - it wasn't really a concern for me, and I hadn't expected that to change when he matured - although it did. What I search for in a horse is character, willingness to cooperate and intelligence, along with conformational characteristics that make a horse fine for riding.
There are so many horses out there to choose from and since I have horses for my enjoyment - both riding and watching them in pasture - I prefer to spend money on ones that are appealing to my eyes. Not my first criteria on picking by any means, but still important.
Large, dark, soft, intelligent eye, wide forehead, small muzzle, thick cheeks, rather small ears, seen from the side, straight or slightly concave profile. If I see a bump right below the eyes, I'll be gone. Every single horse I met which had that bump, was unpredictable.
Only exception profile wise is a standardbred. A standie may have a slight Roman nose and long ears