I would move heaven and earth to find an alternative to euthanasia, understanding that euthanasia is always an option if moving heaven and earth don’t work. Definitely start with vet and farrier. Consider trying to find a companion home with you paying vet and farrier. If your horse is healthy this could be $50 or so every 6 weeks for a trim and a few hundred once a year for shots and having teeth done.
Is the big cost board? If your horse would be happy in a big field with a bunch of horses, can you do a ton of due diligence and send your horse to a cheaper part of the country? In the northeast people send their horses south. Your vet may have experience with particular barns.
On the one hand I would do everything in my power to not put a (relatively) healthy, happy animal down. But if it was truly a choice between feeding my children or my horse, the horse would lose.OP you will feel better about the decision, I think, if you really know that you’ve done everything you can.