So, why are there no lop eared horses?
Actually, there are. The lop ear mutation does exist in the horse - follow this link to see Eeyore, a flop-eared horse.
However, unlike in other animals, the mutation has never been bred for and, indeed, any horses with flop or lop ears are culled out and not bred.
It has to do with equine communication. Horses are so dependent on their ears for communication that a lop eared horse is unable to properly communicate with other horses. The mustang pictured was thrown out of his herd and beaten up because he could not send the right signals.
This might not seem a huge problem in a domestic animal, except that communication with your horse is a two-way street. Horses are large, dangerous animals, and their primary back off warning...is ear position. So, a lop eared horse not only can't communicate with the rest of the herd, he can't properly communicate with humans, making him dangerous to handle.
Hence. No lop eared horses.
(This horse's ears are saying "Hi. Do you have any treats?")
As an ironic note, I found out today that somebody spent money on a study to prove what every 8 year old Pony Club kid knows - that horses talk with their ears. Sigh.