Rendering services aren't available in all areas, but where they are, it really is a good option. It sounds morbid, but the horse doesn't know or care, and it's certainly better for the environment. They generally charge $50 to $200 to pick up the horse.
Whether you can bury on your property depends on your county's regulations, the size of your acreage, the groundwater supply, etc. You can usually find a backhoe for hire in the yellow pages. It's good to have a contact ahead of time so you know you can count on prompt service.
Finally, if your horse passes away naturally or is humanely killed with a single bullet to the head, and it is free of medications or toxins, sometimes zoos, fur farms, houndsmen, or predator sanctuaries will take the meat to feed to their animals.