OP, I have no issue at all with you judging a family because "One of their children has even hit me in the face with stones and has damaged my property . My ds has been kept indoors for most of the summer holidays because they threatened to stab him , and they carry pen/flicks knifes around in their pockets"...In fact I have every sympathy - they sound like a nightmare. And that would seem to me to be a very straightforward reason to contact the police or their landlord.
However, I'm sorry to be a too politically correct for some people's liking, but you can really only judge people by their OWN behaviour, rather than by their predecessors/their race/their religion etc. Very few people would dare complain of these things and tag on the end that the people in question were black or Muslims or Jewish...and we should remember that the Nazis did the same things to the gypsies that they did to the Jews...(end of lecture :) - I dare say it wasn't meant exactly like that anyway). And the fact that they are travellers has absolutely nothing to do with the legalities of having a horse in the garden.
And Loshad, I didn't for one minute suggest that a conservatory makes adequate accommodation for a horse (LOL), I said many horse people have had them in theirs, not kept them in theirs! But there is nothing wrong with a a garage - I know several people who have adapted theirs as temporary living accommodation for their horses when necessary. Nor did I suggest this horse is laminitic - I gave it as an example of why a horse might have its grazing restricted.
As it happens, my guess would be that this family have had some sort of grazing crisis and are doing their best to house (garden?) the horse in the short term. I agree it is far from ideal - but would also suggest that far worse goes on, and that (sorry to repeat) if the horse is happy and healthy it probably won't come to any harm for a few days. Although I would be comcerned about the decking - it wasn't built to carry 3/4 ton of horse and if it put a foot through, it would be very nasty. I can't for the life of me see why anyone would be in a huge rush to call the police (or suggest it had been stolen from a riding school - though maybe it has, who knows?!). But, as has become apparent, there is more to it than originally meets the eye.
I guess I'm a live and let live sort of person. Have frequently picked my kids up from school on their ponies (not sure of the relevence, but responding to everyone now I've started!)...and never poo pick if I can get away with it. So shoot me!