While having a laidback attitude, good trainability and enough substance to resist a horse pushing him around, the most important trait a pony needs is trustworthiness. A horse that will sell you out when the going gets tough will just get everyone in trouble - and that is a trait that can be determined pretty quickly.
To give you a better idea of the process of becomming a pony: I have a horse that is heading off this week to be a pony at EVD for the summer. He’s about 16 hands with a medium build and unknown heritage. He’s probably 7 or 8 years old. I have owned him for less than a week - I traded a mare (not a good pony prospect) for him. I know the horse enough to know he’s a good pony prospect - he’s quiet and pretty sane. He’s broke but doesn’t have much of a handle or a good finish. A pony guy is going to take him for me and he’ll put the miles necessary to make a good pony on him. The discussion regarding taking this horse occurred on the walk over from the backside to run a horse and went something like this: “Hey, can you use a good looking paint to pony with?” “Yeah. You want me to come pick him up or can you bring him sometime?” Obviously, he knows he’ll be getting a decent horse, but as you can tell, there isn’t a ton of thought that goes into it.
The pony guy will probably start him in the mornings with a few to make sure he’s going to be okay and then start taking a few at night during the races. He has a string of ponies (and puts miles on a lot, including the outriders’ horses) and will keep a backup saddled and ready to go in case this horse has issues. But, he’ll just use him - a lot. And the horse will quickly learn to do his job and not worry about too much.
The pony rider taking my horse is an outstanding pony rider - which is even more important than a good pony. He’s unflappable - just sits quietly regardless of what is going on. He can take tough ones without issue and knows how to keep the jock from getting bumped around (letting the rider get bumped by the pony is a good way to have riders refuse to be taken by a particular pony rider). And, you can tell him how you want the horse warmed up and he will do it.
The only true requirement for a pony is to have a negative Coggins and EHV-1 test (and the EHV-1 probably varies by track). They may be stabled at the track or at the farm and be trailered in. An outrider’s horse differs from a pony in that he needs to have enough speed over a short distance to catch loose horses and learn to haze loose horses toward the outside rail (which becomes automatic pretty soon - like a good cow horse).
Everyone I know ponies in a comfortable leather western saddle, but it’s up to the rider and I’m sure the fashion varies by region. I also notice some tracks - like Belmont - have pony people in huntseat. There are restrictions on pony person attire that vary by track and the track does charge owners a pony fee if a pony is used. That fee is debited from the owner’s account, but the pony rider’s fee is paid by the trainer or owner at the time of service (or whatever they agree to).