While Pandeism Fish makes a good point about the inverse-square law, and how the infeasibility of a chicken's musculoskeletal system when augmented to an equine size would lead to the fight being self-concluding.
But we also have to consider the reverse: how would shrinking down to the size of an average chicken affect the health of a horse? And here, we have a pretty clear reason why a chicken-sized horse would be just as helpless as our cardiovascularly overburdened monster chicken. A horse's diet is based on eating a lot of grass. Horses can digest cellulose, which in general is not a very nutritious food (for us at least). I am not exactly an equine microbiological dietician, so I won't give you the details, but here is the common sense explanation: a horse depends on an economy of scale to be able to get nutrition out of cellulose. Its digestive system has to be big and warm and full of intestinal flora to get the needed nutrition out of cellulose rich grass. That is why most grass-eating animals tend to be big. Herbivorous animals, as they get smaller, have to focus on nuts, seeds, and vegetables, which are more energy rich, or have to do things like reingesting their feces, or coprophagy. Horses do enjoy things like apples, carrots or bread for treats, but horses are large enough that they can survive on cellulose. If we were to scale a horse down to chicken size...its digestive system would not be able to extract enough energy from food for it to survive, unless it was eating constantly. Our chicken-sized horses would be just as metabolically penalized as our horse-sized chicken, and would probably be too busy constantly eating strawberries or pellets of their own feces to have much time for aggression, if they could even survive at all.