So, if someone fails to check what their neighbours are doing, that gives them (the neighbours) the right to set off fireworks right next to a field containing several large animals.
Only an utter selfish and arrogant idiot would think that's an okay thing to do.
But hey - it's bonfire night, and they have a god given right - seemingly - to do what the hell they like and who gives a fuck what might happen as a result.
The well being and safety of animals (remember these are large animals, who can't always be easily transported elsewhere, can't necessarily be sedated on a succession of dates "just in case", wouldn't necessarily be safer in a confined (e.g. stable) space) and people in cars as well who could be killed if they had the misfortune to encounter a petrified out of control horse careering into them is quite obviously, according to some, far far less important that the "right" of any old selfish knobhead to happens to fancy some private fireworks.
This kind of complete selfishness makes me despair. This determination to do whatever you want regardless of its effects on others. Any normal person who had unthinkingly done this (and, as I mentioned earlier, they would nonetheless have had to possess an almost unbelievable amount of sheer thickery not to be aware of the dangers) and had then been alerted to the fact by a distressed (and out of pocket) neighbour would have been mortified and apologetic. A decent neighbour would have stumped up the vets fees they caused - yet the OP reports that after she politely told them what had happened they didn't care.
Legalities aside, this is about basic human decency.