On the topic of 'aren't the children upset when their pony is sold', well, yes sometimes, but horse-y children are usually brought up with a slightly different attitude to horses and other working animals (such as farm animals) than to 'house pets' - it's kind of a known fact that sometimes they need to move on because they need to do a job/fulfill their purpose, and so while they may be sad or miss the pony it's not the same thing as if your dog or cat dies or you weren't able to keep them.
To be clear, this is NOT saying that the children are in any way allowed to think of the animal as a disposable commodity or that their welfare doesn't matter, quite the reverse, for a farmer or someone who relies on their animals for their livelihood the care of the animals always, always comes first, even before that of the people (which is why I imagine it's really hard being a farmer's wife or child!), it used to be the case (and still is in some parts of the world) that if your plough horse or dairy cow or other working animal got sick or died, your whole family could literally starve and I think the attitude persists even to this day. I'm only a leisure rider myself but was brought up on the first principle of horsemanship (and taught my children the same), which is you always look after the horse before you look after yourself. So for instance if on coming back hot and tired from a ride, if you were caught getting yourself a drink before you'd taken your pony to water, you'd get an almighty bollocking from your parent or teacher. On cold or wet days you might want to stay indoors but your animals need to be fed and mucked out so it isn't a choice - in exchange for them working for you, you need to take care of them. Like I say, a different relationship to say a dog where the connection is perhaps more emotional/familial but also less like work on both sides of the equation! People are equating the horse/rider relationship to a marriage, for me its perhaps closer to a business partnership, you have to look after one another and get on well together, you have to communicate well etc., quite often (but not always!) you are friends as well as partners, if one party gets sick or old it's right that the other ensures they are cared for, but it isn't something that necessarily can or should go on forever...
Of course there are bad horsey people out there and you do get people that weren't 'raised right', that do think of all kinds of animals as commodities/playthings - small point but for instance, it drives me mad when kids hand their ponies over to a parent or groom after their ride and aren't interested in making sure the pony is comfortable, but that isn't proper horsemanship and so in my mind anyway they aren't 'real' riders anyway 