Horses can and will take meat if offered it, even though they wouldn't eat it in the wild. As far as we can tell an occasional bite of hamburger won't hurt a horse.
However, they aren't evolved to digest it and it's likely that at best it won't give them any nutrition, at worst it might make them uncomfortable. (Horses don't have gut bacteria to break down meat protein, so it's certainly not going to do them any good).
Personally, I don't recommend giving your horse a bite out of your ham sandwich. He'd rather have an apple or a carrot, after all.