I know this is going to sound strange, but how about a mini??? We have an "R" mini, 36 inches, that we got when he was almost three, and started working with him right away. Our area has dogs that people just run loose. When the first time I walked down the road with him, he was scared of everything. Well, after the 100th time he knew every single dog, and would just walk right past them, like it was no big deal. So at three and a half, I put his saddle on when I'd walk him, over and over and over again. I'd walk like three miles a day with his saddle on him. He loved to go out with me and check out his neighborhood and his dogs... Once he got used to having a saddle on his back, weight wasn't a problem. The most difficult thing was the introduction of the saddle... (and him sticking his belly out so I couldn't tighten the girth)..
Then each day, I let one of the kids, (usually the littlest sit on his, while we fed him treats. He got to associate a kid on him, with treats, so he was happy to see the kids coming in his direction. Of course then I started walking him with a child on him, progressing the weight of the child. (up to about 20% of his weight).
So to speed up the story, when we evacuated from hurricane Jean, I took the minis with me to a Motel 6. I would take them off the trailer every four hours around the clock and walk them. Well, there were about 1000 kids that were in the motel along with other motels on the same block. It was known pretty fast that I was out there, walking the boys, and kids were coming over for mini horse rides. Our gelding was such a good boy, and ever after midnight, parents were bringing their kids to ride our mini while I was walking him. We had no problems whatsoever. If it had not been so close to a highway, I would of let our nine year old ride him, instead of lead lining him.
He's such a good boy.... We're so proud of how he went from obstinant stallion to sweet rideable gelding with no problems at all. He was much cheaper then any pony I can think of would be.