..mmm....I think maybe the protests are mostly aimed at WILD animals, tigers, elephants, lions etc...........not so much at horses which, though they may have been WILD in the ancient past, are now regarded as domestic animals which are part of the human scene as are dogs and cats etc.............just my view of it. ;-)
And by the way...there is quite a lot of protest at such as the Grand National which is the branch of horse racing which pretty dangerous compared with merely running round a grass track..........again IMO.