If I had a good reason to not want anybody taking pictures of my horses, I wouldn't put them in a pasture close to a public road, or I'd at least post a sign saying not to photograph them. If I had an extra good reason, I'd put them in a barn or somewhere tucked away and protected from the public eye. If I really, really had something serious going on, I'd probably keep them covered up (full flygear in the summer, sleazies and rugs through the rest of the year) or disguise distinguishable markings or buy only very unremarkable horses...maybe if someone had a hit out on me and I knew of some way to identify me by my horse, or perhaps if I were a horse theif
It's very silly to think that your horses are incapable of being photographed without your permission with drastic measures are not being taken to prevent them from being seen by anybody. Neither is your house or car or other animals...neither are you.
When it comes to posting a cute picture of a random horse in the middle of nowhere...I can't think of any valid reason to care (unless you would be in danger, in which case see above) except for just being sort of a wet blanket and saying "because he's mine". If your horse is in the view of the public eye, face it, anyone can see him. Who cares if it's through a photograph or in person, that horse is visible for complete strangers to look at all they want...even go home and update their blog about the silly horse they saw whilst out driving today, along with a very detailed description. Is that immoral too?
To the point, by all means, I'd be very pleasantly surprised to come across a photo someone took of my horse online, assuming the photo was, as described, taken from public property with no trespassing on private property and no one was claiming him as their own or publicly accusing me of poor care in an unjustified situation or, of course, making money off of it, or calling him butt-ugly (even then I'd just have my little feels hurt for him and agree that they were entitled to their own opinion, no real harm or fowl)
One of my favourite things to photograph these days is random cattle in the middle of nowhere. Honestly, I've usually been known to stop dead in the middle of the road, roll down the car window, and crank up the zoom. I've done the same with horses, though I usually get enough of a "fix" taking pictures of my own horses at home since I can get them to run around like wild things and pose for me
Now that I certainly wouldn't do with a stranger's horses!
Wow, kind of a novel....it's late, I ramble!