As long as he's a "colt," I wouldn't be formally jumping him. I allowed my long yearling to step over a crosspole once or twice at a clinic but that was purely for the mental exercise, there was no strain on his front legs as he didn't even jump it. Now that he's a long two year old we've been working on learning to cross ditches, step over small downed trees, etc., and of course he tends to jump those but he's free to cross them in any way he chooses. I figure if the horse is doing only as much as he would naturally following the herd, isn't forced, and is free to stop or object at any time then it's unlikely to harm him. You should see the shenanigans he gets up to when playing with my older gelding!
Spinning, leaping, rearing, sliding halts...wow. Quietly popping over a ditch in the course of coming and going from our trail walks once or twice a month is unlikely to hurt him compared to that.
Still, I would not want to see formal jump work over any kind of height until the horse was at least 3 years old. Especially in deep footing, that's a lot of leg strain and the higher the jump, the more damage there's likely to be. Working with us on a lead rope or carrying a rider throws them off balance and places much more strain on their bodies than free jumping in a natural situation where they can use their heads and necks and find their own balance. I look forward to starting my three year old over fences in a few months but he's mostly going to do basic gymnastic routines over low cross-rails and only a few times a month to help him develop some rhythm and power. By the time he's four he can handle full jumps and I won't worry so much.
With a full-sized horse "jump work" tends to mean full formal workouts with a rider over courses in an arena. IMO our minis are being asked for far less and aren't as likely to get joint damage from what we do in early training but there's still a very real risk of introducing muscular tension, spinal misalignments and other things that will cause a young horse pain. That's why I follow the same guidelines despite the difference in activities.
Leia