I believe it is now illegal in NY, but I do not know the details in regards to the law.
I had to put one down on Sept 10th of this year, was one of our best jumpers, maybe 8-10 years old, he had a tumor on his left hind quarter that was just taking the life out of him, vet could do nothing, they get $250 I believe, to do the procedure.
This fellow was brought over to a small hill side, sedated, I was above him, for safety reasons with someone holding the lead shank away from bullet trajectory. A properly placed .38 caliber bullet from a snub nosed revolver, is as humane as it gets, he dropped and died instantly. It's not for the weak of heart, but when you have an animal that is suffering with no chance of recovery, it is an ugly part of the responsibility. Our vet was on the premises for another horse and absolutely agreed that done properly like I did, was as humane as any other method, off the record stating, it'll just cost you if I do it, and I will if you need me to, but regardless of the law, these things we do as we see fit. No animal is to suffer, what has to be done is done.
You must take care to make sure the shot is placed properly, sedation is necessary in my opinion, there is no suffering, they just drop. You have to be mentally prepared and be able to do it without hesitation, you just don't have any other choice sometimes, what happened to this particular horse we have only seen one other time, in 40 or so years, the other one recovered, the vet did everything possible and we kept him going til it was time. We have someone who takes the carcass, they place them in a manure compost pile for over 1 year, they are a legit business and abide by the state laws to provide removal services. I find that when one goes away, I build something in his memory, for him it was a small table for our tack room with a rough sawn plaque for his nameplate, it helps me deal with it, and the horse has something dedicated in it's memory, silly as it sounds, it is what I do.
I've got 2 others, one with a fracture, dumb@ss help mistakenly turned him out with another that had hind shoes, something we just don't do period because of this, looks like a kick did it, and he's healing nicely, but it could have gone the other direction, been 2 months now, but one wrong move and there would be no time for a vet to come, shameful part this horse was coming along nicely, all the riders adore him, great personality and ability. He's on stall rest but it's like walking on eggshells, you just hope you can get past the danger, or he's done.
The other we can't yet figure out, vet thinks it is neurological, and has treated him as best can be done, it was suggested that he be put down, he's sound again, but now just tossed a shoe and screwed up the hoof, he too was coming along nicely, excellent jumping ability and confidence, not the easiest going personality, but smart as a whip and confident. It appears to be some very odd occurrence as to the lameness which was intermittent.
It's all part of the game, we are very fond of the string of horses we have, we provide the best we can for them, so it is very difficult when one of them has to go, and I'd admit that with a few of them, it would appear to be very difficult to do this myself, unless it was a situation where an injury took place, causing suffering, I'd not hesitate. Someone has to do it without hesitation, in some cases it may be best done by the vet, regardless of cost because a person does get attached to these horses, it's not easy no matter how you look at it, I sincerely wish you the best of luck with your situation.