Presumably for the same reason that hunt sabateurs spray substances at hounds that irritate their nose lining so they can't follow the scent of a fox, or lay false trails that in one instance resulted in six hounds being lured onto a railway line and killed by a train...
I think most protests attract the hooligan element. There is always a minority that don't really care about the issues, they are just there to cause trouble and hurt the police.
These are the ones throwing bottles at horses - not the actual animal rights activists.
They also in many instances get paid by The League Against Cruel Sports to attend these protests along with a packed lunch, I had these protesters throwing stones at my dogs just because they were playing in a stream adjacent to some hunt followers.
Because some people are so blind to their cause they do not think about the consequence of their actions. While they are busy thinking about preventing animal cruelty or fighting for animal rights there are no thoughts going out to the horses who are forced to work with the police. How often are there protests against people throwing things at police horses? Hypocracy.