I am so very sorry for this tragedy
Since the horse has not been moved, get pictures of the entire horse from all angles and also the bullet wound, if you can. You should also take pics in a broader view to show the angle of the horse from the perspective of all of your boundary lines.
You want to establish the direction the bullet came from - or whatever device they used
That may or may not be a crucial piece of evidence if this gets to court.
I would also be contacting my family attorney ASAP. If he/she is not comfortable with this case, ask for a reference of someone who is familiar with this type of crime.
Hopefully you still have your receipts. If this was a show horse of any venue and you have any ribbons or trophies to show future potential, take pics of those for your lawyer.
You want to establish as much earning potential as possible and if you win a judgement and the Loser does not have money in the bank? BY ALL MEANS, put a lien on
his home, his car, his farm tractor, his breeding dog if he has one. ANYTHING to where you can get compensated once he sells whatever you put the lien on.
Of course that will require you keep close tabs on him, so nothing would slip thru your fingers.
Good luck to you --- my very deepest sympathies