Our foals were taught from when they were born to give to pressure and we never had one set back when tied.
Some of them at times we ponied them for short rides, at times from their own dam and they were fine.
They seem to have a great time going along, very curious and happy like.
It is all how you do things, be careful, as explained above, the trick is not to ever get in any fight, but finesse any time there is a bit of problem with a youngster, especially careful that they don’t feel too much pressure from the halter.
Very young ones can panic and flip and get seriously injured.
Teach to give carefully and keep reminding them about it, always gently.
Sounds like yours is already there with all it knows, where ponying should just be one more fun thing to do.