Maybe the OP can't afford to take care of him. It's been stated a couple of times she'd have to dip into her emergency fund to euthanize.
I'm all for helping out animals when I can. I am a firmer believer in it. But my feet are also planted firmly on the ground and if I can't afford it, I can't.
OP I'm sorry this happened to you. It puts good people in an impossible situation. If you can't afford to hang on until you get him placed, I'd go with the shotgun/hand gun route. If you don't have one maybe someone you know does. Course the problem is burying him apparently and I have ZERO ideas on that. We just got a backhoe to bury ours on our property when the time came but that itself cost a pretty penny even way back when.
And, yeah, it is a matter of expense. I can afford to keep him a few days and see if someone'll take him, but I can't really afford to keep him past that. I've got limited hay, no free stalls (goats due soon), and a limited amount of money for emergencies, which I don't want to dip into if I don't have to. Things tend to happen this time of year, and I'd rather not spend half my emergency fund (when it's all said and done) on a horse that isn't mine, only to have one of my own animals get sick/hurt.
I am sure I could find a shotgun if I needed to, but we rent property near an airport. The landlord has asked us not to bury any animals, and we're not allowed to set fires due to the airport. When we have smaller things die, we usually take them out to the woods and the coyotes have them gone in a day or two, but a horse and a goat are drastically different sized, of course.
This certainly wasn't really what we needed right now, haha. If it were in the summer, I'd be fine with holding him until someone could come get him, but with no shelter and not enough hay to go around, that won't work. Then again, people don't dump horses in summer, do they?