Formal:
* Senior horse: This is the most neutral and respectful term.
* Geriatric horse: This term is often used in a veterinary context.
Informal:
* Old timer: This is a common and affectionate term.
* Veteran: This implies respect for the horse's long life and service.
* Grandfather/Grandmother: This is used for horses that have lived a long time and may have offspring.
You could also use the horse's name with a descriptor like "old" or "elderly" depending on the situation.
It's important to remember that horses age differently than humans. A 20-year-old horse is considered quite old, while a 30-year-old horse is truly a senior citizen.