You do need a solicitor if you cant come to an agreement with the owner.
The owner would have to demonstrate that negligence lead to or contributed to the horses death. Accidents are rarely simple single events and normally have several contributing factors. Providing more information on this...
What breed, height and colour is the horse, as all these things will alter its value.
Its it happens to be an good height, pure ID in a desirable colour or PRE its likely to still have a good value.
Im going to go against the grain aswell
Welsh A's are generally pretty, by prime age im assuming you mean desirable age around 10 (?) so not a baby or an OAP and depending on her colour, this may add value aswell. The pony is backed but fast, sharp and can jump, but will also go on a lead rein...
Im assuming this is what you've found?
https://www.allbreedpedigree.com/thorneyside+flyers+magic
http://www.rainhillwelshcobs.com/profile.php?name=Thorneyside%20Flyers%20Magic
This is exactly the same as what happened to one of our ponies (he was a cob X) it took about 3 - 4 months to sort and around 2k (this was several years ago) in vets and vets farrier, but he came good :)
I think my main question would be - has the horse always had these issues or is it a new thing? Also what is the pony's postives (this will add value) and the other ponies you mentioned in the 2k comparison have other issues
My pony had one like that on his sheath, that my vet removed (cut it out) by standing sedation in his stable and sitched up the wound. I dont remember it getting infected, but he was on pain relief and antibiotics for a good week or 2. They did grow back slowly, but he was an older horse and was...
slightly over budget and probably not backed
https://www.preloved.co.uk/adverts/show/122418467/3-yr-old-irish-draught-sport-horse-pot-showeventallrounder.html?link=%2Fsearch%3FsectionId%3D3365%26advertType%3Dforsale%26page%3D3
Im really sorry about your cat, but id have to do something because this could happpen to a child! The dog should be muzzled and on a lead at all times!