I read an article in a magazine once about a Mustang they named Eeyore, who had floppy ears similar to this. It was a deformity that he was born with, and because he couldn't communicate with other horses, or rather the other horses couldn't read his body language, he became very aggressive towards them.
I think he even got shot by someone (he had bullet fragments in his tongue) because he attacked the horse they were riding. Eeyore ended up getting rounded up and getting a good home and training though, so all ended well.
It does look kind of cute!