Domestic/professional horses live in stables, which are much larger than a trailer and generally have access to fields etc, get out for a run regularly. I am sure some people abuse their horses, but a good standard of living is absolutely achieveable in a stable/yard/field type of environment. I'm not sure you can say the same for much larger animals living in accommodation which has to be easily movable etc. It would be like expecting a horse to live in a horse box all the time, that wouldn't be fair.
I wouldn't object to the use of smaller, easily trainable animals in circuses - dogs for example can be trained to perform very nicely and without the use of pain/fear type techniques, and can also be perfectly happy living in a caravan sort of environment, as long as they have human company and get out regularly for walks, which would be totally achievable - you don't tend to see circus tigers, elephants being taken for walks! How could you do that? It wouldn't be safe for the animals or the general public. And it's cruel to keep such a large animal cooped up in a trailer all the time except when they are performing. You couldn't have an elephant or a tiger living with the circus performers/trainers in the way a dog can, because they're just too big.
I don't know much about horse training so I have no idea if things have moved on from pain/fear/force - I hope so. I would like to see that kind of training outlawed anyway and if it means that we lose any type of animal-based entertainment, that's fine by me. I also don't know enough about horse keeping to be able to judge whether they could have a decent standard of living on the move. If the animals can be trained in a respectful way and have a good standard of living, then there's no moral issue with it IMO. But I just don't think this is possible with the larger animals associated historically with circuses.
Dogs, small monkey breeds, birds, rats, maybe horses - all seem reasonable for circuses to me but I think as things currently stand it's probably just easier to have a blanket ban than to specify that it's OK as long as the animal has a decent standard of living and is trained ethically.