All horses lose health (and skills) every aging after 25 years unless they have a philosophers stone. They die when their health reaches 0% (there is a risk of them dying at any point with <5% though). If you just groom, feed and bed them they lose 2-3% health each aging and live to 32-33 years. However, if you enter them into 6-7 competitions each day, feeding correct amount and bedding with at least 20% energy, the only lose 1% health per aging and live to approx 38 years.

You can reset a horses health back to 100% by using a black orchid BMI but this is a reset and the horse will then continue to lose health with every aging after. It would be possible to keep a mortal horse alive forever assuming you had enough black orchids to keep giving them. At that point it would be more sensible to just give them a philosophers stone to make them immortal.