His name is Rocky He's 30 kilos of pure muscle, so when he jumps on you to lick your face it can be quite painful, but I miss him so here's one last picture :P
In other words, the horses which can be seen above are not really your pets. But you have a strong affinity to these horses, so much that you regard them as your pets?
Just because most people don't own their own stable to keep their horse in doesn't mean they aren't their pets. If you own said horse it is still your pet, even if it happens to be in "rented accommodation" so to speak.