See I'm a firm believer that animals and humans belong together- when appropriate. There are reasons horses, dogs, cats, and other animals have been "domesticated" and other animals have not. I live a few hours from a reservation that has wild horses on it.
When the economy went down, people would actually release their horses into the wild because they couldn't afford to feed them anymore. Unfortunately, these horses were not adapted for the harsh winters without blankets, the lack of food, and the absence of veterinary care that had once been available to them. Yes, some of the horses survived, but when, in the past, we had driven through it was a surprise and exciting to see a herd of wild horses, now dead horses are almost always seen on the drive through, along with so many herds of horses there is no way the land they live on can support them.
Additionally, if you knew what horses went through when they were shipped to slaughter outside the United States, I think you would see how many feel this option is a horrific one. I wouldn't post pictures of examples because they are all awful.
I'm not into using animals as transportation. Horseback riding is one thing, but a single horse pulling a family of four is completely barbaric. I see your point about the working horses not having a future if the business is shut down, but there are plenty of ways around that. I'm sure there are wealthy New Yorkers who would love to adopt these horses and give them a lovely home. With the technology and machinery we have nowadays, there's no point in forcing animals into labor.
Horses as a general rule can actually pull up to 3 times their own weight on wheels over paved ground. Most carriages weigh between 800-1000 lbs. Most carriage horses weight between 1200-2000 lbs depending on whether they are a light breed or a draft breed. Even miniature ponies are easily able to pull carts of up to 2 people- usually a parent and child with a very lightweight cart (weighs around 80-150 lbs). I own two miniature horses that are freaking hilarious with explosive manes and just cuteness all around in general (pic below). Usually we just have them for cuddles and love, but occasionally we'll throw a miniature pony saddle on them and take my 3 year old daughter for a ride.
Cuteness alert below.
If the horses that were pulling carriages in New York were guaranteed a happy life afterwards and the individuals whose entire livelihood rested on their carriage horses were able to find a career that didn't displace them too terribly, I would be an immediate advocate of their removal from Central Park. I just find it frustrating that the people advocating so strongly for their removal aren't doing much to set up everyone that will lose because of this. I guess I look at this with the ethics of the a Utilitarian. Some must sacrifice for the greater good...I dunno. I'm torn really.