It may be a sad topic, but it’s also a necessary and practical one. It’s always better to know ahead of time what your options are.
I’m lucky enough to live on a farm and all my horses are buried here. As others have said, you don’t want to be there for the removal. If it was someone else’s horse, I’m sure I could help do the bundling and even be there to help maneuver them onto the truck, but my own horse? I don’t think I could. But then again, when I have to put my cats to sleep at the vet, I’m there for the last bundling into a blanket before I take them home to bury them - it’s like the last little thing I can do for them. But if it involves a tractor and chains and - just no. Just don’t be there.
I’ve been present for all my horses, and each one is different. Your vet should be able to walk you through each step as they do it. Mine does. “This is the sedative.” “This is the euthanasia.” “Here’s what to expect as the nervous system shuts down.” I know by now every step, but my vet does it anyway. It helps. As @endlessclimb said, the sounds and movements they make can be troubling.
There is no shame in letting someone else your horse trusts hold that lead rope. Or in letting the vet give the sedative and then not being there for the actual euthanasia itself. You will have a few minutes in between them to remove yourself and not hear or see anything further. Once sedated, your horse really won’t know if you’re there or not.
When it became crystal clear that my dad’s dog had to be put to sleep, he was still resisting it, but I finally made the appointment, told Dad I would take him, and I think that was the key - he didn’t want to make that call, he didn’t want to be there. Once I said I would do it, he was easier about it. He knew, deep down, it was the only choice, but it wasn’t a choice he wanted to be responsible for making.
Your vet will know who to call to remove the body, and what options are available to you. It’s better to have the information now (and on file with your BO and vet) than to not have it when you need it.