I went with western saddle to start the kids, about age 5-6. Had the horn to grab, suede seat for grip, 12 inch seat length. Nice brand name maker, Billy Royal. Then their saddle size went up an inch at a time as they grew. 13 inch to 14 inch, ending with a 14.5 for the girl, 15 inch for the boy. Saddles fit them right at that growth stage, I never bought saddles for “them to grow into”. Can’t ride well if saddle does not fit the rider. To buy one now, I would look at barrel saddles with small seat sizes. I have seen them on Ebay for pretty reasonable prices, below $500. Other saddle sale sites will also have them for sale. Might even find one locally on Craigslist. Those little girls outgrow them soon, so not really worn much. AND they have trees to fit bigger horses, not all smaller pony sized trees. The barrel racing folks who start them early, are serious about good fit for child and equine to get the best speed in a go. Talking about winning BIG MONEY, so saddle fit is serious business to them.
I would think a Haffie could wear western saddle very comfortably. I WOULD add a Y-shaped breastcollar for safety, saddle can only slip so far, not under his belly if something happened. My kids ALWAYS used breastcollar or hunting breast plate when riding as a safety measure on their western and english saddles… Even as they got older, they might get distracted as kids do, forget to recheck girth, tighten it again. I could not always be there to remind them. Happened ONCE to each kid at about age 13-14yrs, saddle slid to the side, breastcollar stopped saddle, they swung feet down to get off. The same wonderful older horse stopped dead with kid hanging on saddle on his side, waited for saddle to be fixed. They got embarrassed because it happened at workouts in front of friends who razzed them about it! Have to say our kids never forgot to recheck girths again, and I saw more kids at workouts checking their girths without being reminded!
Western saddles have a nice seat to aid a child to stay seated with the higher cantle, swells in front under the horn. I would not worry about posting so young, they have hands and minds full, with reins, keeping feet down in place, steering and helmets unbalancing them. Little kids have a lot of body weight in just their heads, easy to get off balance just turning their head to look at you! I used a mechanical hackamore, western type with a thick covered nose, long shanks, so little kids were not pulling on mouths. I wanted child able to easily stop horse with a pull, using their small strength.
Mine learned to post well after learning a secure seat, control of steering, better coordination with age, confidence in being in control of their horse. Both continued on, learning English riding skills, enjoyed jumping, hunt paces, showing.
I did not let them ride without a side walker until they could hold on, stay seated when horse did a full body shake. It was a measurement of body strength, ability to think to grab the saddle horn if needed. Their small horse would shake herself starting almost every ride, so I held them on, in place, before they could do it themselves. We laughed each time, said she was making sure everything was in the right place. But it would have been frightening if she had shaken them off because they were not strong enough to hold themselves on. Son actually was not as strong as daughter at the same age. She just grew bigger, faster, sooner. So I just went slower with him. Age is not a good measuring tool for ability of body or coordination development. You have to work with the kid in front of you to keep them safe.