I’m very sorry for your loss.
I think the first place to start is to determine if the horse was insured. Typically, expensive horses are insured for both mortality and health. That insurance policy could be an indication of the value when purchased since purchase price is usually the insurance value.
Second, pretty much everything to do with horses costs money. This does not necessarily increase the value of the horse; however. Early, training can increase value. Show performance winnings can increase value. Teen age, arthritis, injuries, ect decrease value. In fact, it’s difficult to even find insurance on horses over 15 years old.
You should expect to pay between $1,000-$2,000/month or more; for board/training/farrier ect. in Texas. Most trainers charge around 15-20% commission fee to sell a horse. A through Veterinary exam might be prudent since buyers will want xrays ect and any limiting findings can impact value.
Third, there are Equine Appraisers the estate can hire, if need be, to determine value. I’m not sure the cost in that? Maybe in the mid three figures?
In order to minimize expenses for the estate, it’s probably best to find out a realistic value and find the horse a good home. Hopefully the current trainer can conduct the sale process or recommend someone reliable. Luckily, it’s a sellers market.
Best wishes!!