Leasing a horse is a wonderful option, but what happens if you start to get attached and want to buy your leased horse at some point? If you don't have an option-to-buy arrangement in place beforehand it's all up to the horse's owner. If you've been leasing for a while and put lots of training time or gotten emotionally attached to your leased horse, then sadly there's a good chance that the owner could ask for more than the horses real value or be uninterested in selling.
To avoid this situation, consider asking for an option-to-buy before leasing a horse. Before you have invested your time and energy ask what terms might be acceptable for an option-to-buy. A price can be determined based on what the horse is worth before you start leasing or get attached and a timeframe can be set for when a decision will be made. There are hundreds of possibilities for an option-to-buy arrangement that you and the horse's owner will have to agree upon, but it's well worth the trouble.
If the owner isn't interested in selling, weigh your options: lease anyway or keep looking.