Firstly, feel free to pick and choose from the SRD, obviously! Ignore what you don’t like, take what you do & reshape it to fit.
I think the main reason for emphasising ‘the object cannot act alone’ is that you can risk devaluing the influence of the agents if the object can just do whatever it wants, whenever it likes. But here, clearly you’ve got an animal that is typically in servitude to a rider, so I think it should work really nicely. Sure, your horse might spend a year running around in the moors, but eventually the story will pick back up when someone comes to ride them again.