Ouch.. Baaaad situation x_x
I agree with what has already been posted. I hope your boarding agreement covers it.
I have an air-tight Boarding Contract and I allow 5 slots for emergency contacts (and encourage more just in case). I encourage them to put numbers for their family, as their family members would also know what the owner would want for their horse. I require 3 Phone Numbers from my Boarders AND 5 emergency numbers. Its one thing if, like appylover said, the horse had an injury and you couldnt get a hold of the owner and you decided to let the vet stitch the injury up. That's just a vet bill the owner would have to pay. But euthanasia.. I mean.. not only will the boarder have to pay the vet bill.. BUT they will also have to pay for removal/burial/cremation/etc, AND find and buy another horse if they are ready to move on. Not to mention, deal with the mental anguish of not having closure, especially if it was a sudden death like it seems your describing.
I would feel pretty upset and almost betrayed if I was boarding my horse somewhere and he/she was put down without me knowing. I would hope that if I was still boarding my horse somewhere, the Barn Owner would choose to ship the horse to the hospital rather than put it down. At least then I could call the hospital and say "Heck no, I can't pay for it!! Please give me some time to make it up there so I can say goodbye and we'll put her to sleep." With my boarders, I ALWAYS assume they will choose to pay any expense to make their horse get well. Infact, that's also mentioned in my contract, lol!
Also.. was the Vet that put the horse to sleep the Barn vet, or the Vet that the Owner recommended for their horse? Where I live, the county vets always recommend Euthanasia for the bulk of the wounds they encounter (no joke.). I would have wanted a second opinion if a vet told me I needed to put the horse down (unless the horse was in a ton of pain).
Always, Always, Always assume the owner will take the option of life! Lol!
Best of luck to ya!