When I bred them and I had transport them anywhere, we used my full sized horse trailer. Now, I no longer own one mainly because I had no use for it. I have been playing around with a getting a small trailer (U-Haul) looking and transform that into a mini horse trailer.
Now this is something I would done professionally so do not worry. I would need to get a devider put in, some windows, vents as well as padding. To look into, it shouldn't be to difficult to do. BEcause it would be under the 2,500lbs limit I know I wouldnt have to add a breaking system in.
To be honest, I don't know for sure that something like that can be done but I do know a lot of miniature horse owners who will carry and put the horse in the back of their truck or have done many other genious things to transport them. Let's put our heads together.