Maybe the Amish are largely brought up to regard animals as food, or as tools. I'm not necessarily agreeing with their outlook on this, but I can see the value of it in some lifestyles. I understand the Indians were much the same way, for the most part. Their horses were mostly utilitarian and not so much a part of the family. I think its just the modern, more politically correct view now to think of animals as pets or family. Most settlers could not afford to keep livestock animals as pets and, thus, animals were viewed with much more practicality. In lean times they were food, if hard work was required by them to keep the family from starving...well, tough on the horse.
I don't think the Amish are allowed much frivolity in their religion and lifestyle. Sentimentality is not a trait they tend to cultivate, either, I believe. As they have different cultural beliefs in these matters, they can't really be judged by our standards.
If a culture that worshipped cattle were to view America's massive intake of beef, they would likely feel we were quite the barbarians. Its strange, really, how folks think its okay to kill and eat a cow, chicken, pig, goat or sheep but draw the line at a dog, cat, or horse. In some places dogs are worked very hard each day and fed just enough to keep them alive. China raises dogs for eating. I can just see people in America harnessing up their fat canines and expecting them to run most of the day. Or eating a Pug Pie!
People's treatment or handling of their animals is largely relative to culture. The Amish, I'm sure, feed, water and provide medical care for their horses, if only to make sure they are operating properly for the next work day or trip to town. I don't think they are either good or bad, really....just different. And that's not a bad thing. I'm sure they view our keeping our animals long past their usefulness as being quite wasteful of time and money. Maybe time and money that could be better spent on their family's medical care, or something equally as costly.