Here is a bit of practical advice …
As has been mentioned, you need a plan for what happens to the body afterward, a plan made and scheduled beforehand. It can be hard making those phone calls, setting dates & times, but just think of it as part of the process, as with so many other things you have done for your horse over the years.
If you want burial on your property, know that there are some regulations in many areas because large animals buried in the ground can have effects on the ground water. However if this is the first one on your property, I wouldn’t worry about that too much. If the grave(s) aren’t visible from another property or the road I might pass on the whole drama with regulations, a drama which I think is sometimes over-rated. What they don’t know … but anyway just a heads up.
There are cremation services if that suits you better. But not as many for horses as for small animals. You need one that will pick up, so it may depend on what is available in your area (or your horse’s area if he doesn’t live with you).
Cremation for a horse yields such an enormous package of ash/etc. (not necessarily all your one horse) that you might prefer a simpler small box of ash and some tail hairs. These are options the service will discuss with you. The price varies significantly to get more back.
Which brings us to the next ‘what do I need to know’ point –
You need to plan in a fair amount of detail where, when, what else and who else needs to be there, as well as how.
Where will the body fall, how long will it be there, do you want to cover it and with what, how accessible is that location to whatever will move the body its final rest. Who must be there and when (pick-up service, backhoe), and who do you just want to be there for support. So that is a lot of setting dates/times and gathering necessary things.
If you need a lot of ancillary services or assistance, and/or your horse is not located close to the services you want/need, euthanizing a horse can turn into a coordination effort like a community picnic. Hopefully it won’t be that complicated.
My last horse’s home barn didn’t allow burial on the property, and was (surprisingly) a bit squeamish about the euth taking place there. Even out of sight of anyone who was not involved. So my initial idea of letting him go peacefully in back of his own barn, with a cover over him until a pick-up service could come, became increasingly awkward. Especially sensitive was the time the body would be there until pick-up, even covered and out of sight. Would never have guessed they would have this outlook. They had many horses on a large property and of course lost a few over the years. But they were remarkably not helpful or prepared for a boarder euth.
In addition, the barn was too far away for the pick-up service I wanted. After calling vets for references (some had some, some didn’t), scouring the internet, etc., I ended up with a different plan.
Early in the morning I trailered my horse 25 miles to a vet clinic who was in the pick-up range and was agreeable to euth, and to allow the body to stay in place, covered, waiting for pick-up. My horse was totally agreeable to load & go, he always enjoyed an outing. Fortunately the weather was a very pleasant day. I was prepared to spend time with him before the euth with peppermints and his favorite scritches and chat.
That’s how it finally worked out. I was very grateful to the accommodating clinic.
. My sister wanted to be there “for moral support”, but I respectfully declined. It wasn’t my 1st euth (unfortunately) and when my vet arrived she was glad it was just her and I, since she had been at euths where the whole family was there and the horse was totally stressed out. (We were together alone at the insemination so it only made sense we were together to let her go). Once the sedation kicks in, the horse isn’t too aware of who’s around anyway, so you could give the lead to a trusted helper and leave to deal with your feelings at a spot your horse can’t pick up your stress.
