Anatopism - welcome to the thread and I'm so glad yo've had such wonderful CT experiences! It's an exciting world of training when it comes to horses :) I did have a few thoughts reading your post:
It's exciting to know that it can be just as successful with a horse, and plan on leasing a horse in the near future for the first time, and hope to practice some clicker training with him.
Just throwing caution to the wind here - because you're leasing the horses, you may run into a few issues. I don't know if you plan on leasing your horse for the rest of its life, but if not, that means it'll eventually go to someone new. While I prefer CT, I don't know that I'd CT a horse that I didn't plan on keeping because I don't trust that the person who got him after me wouldn't continue that training. You'll have to talk to the person you're leasing from about this.
I imagine that a horse that has been trained using "traditional" methods would adapt back and forth easier to whatever the next person's methods are, but continuity and consistency in training and handling is so important to horses. On one extreme end of the spectrum, with a young horse still at a critical training stage and only ever having been exposed to clicker training, it can actually get dangerous if I don't have my clicker with me and we try something new to him or even just something that he hasn't practiced enough because he'll try more and more behaviors thinking he hasn't figured out what I want yet and get frustrated because he just can't get it right. He doesn't understand the release of pressure as a reward because he was simply never taught that way. Not only would we have to start from square one like a new horse in training, but I imagine it would be much more difficult than beginning with a "blank slate" because he already has formed his ideas about how the world and training works using CT. I guess this is one downside of using CT before teaching a horse how negative reinforcement works, but Flash is my forever horse and I don't even know if anybody but me will ever even work with him much less own him.
I doubt you will run into such extreme consequences of using a clicker training with your horse, but it is something to think about. You'll have to decide what's best for your horse and its situation. (Even outside of clicker training, this is one of the difficult things about anyone using a new horse whether a lease or just borrowing for a ride - everyone rides and trains differently and I trust very few people to work with my horses, including the traditionally trained ones!)
I do have a question as far as age of horses go. For everyone actively posting here with there experiences... do you find it more or less difficult to CT a horse who has 'been around the block' so to speak, and does not push their limits, or try as many new behaviors, as compared to Jillybean's Flash, who is completely new to all forms of training, and more likely to offer new behaviors to capture and shape? Is age a factor in how you approach CT with a horse, or is the individual personality of the horse still more prominent?
This relates back up to what I said earlier about having a horse that's only ever been trained using CT - you may actually have an advantage by teaching CT to a horse that's "been around the block". It does take some transition time to re-wire their brain to understand that offering behaviors is a good thing, but it can be done fairly easily. Most people who do clicker training (or own horses in general) don't start with babies like I do. I've been helping my dad train horses since I was 10, so I wanted to start with scratch with my first horse and so bought a baby that'd only been halter broke. In fact, not only are most people working with horses that have "been around the block", but some of the best success stories (ask PunksTank) are about horses that have been around the worst blocks and aren't only wired to respond to "traditional" training but mainly behave the way they do out of pain and fear. You couldn't get farther than that from CT, where a horse learns to feel comfortable not only doing what he's been told, but also comfortable enough to try new things!
Since operant conditioning is a natural thing to all living creatures, you're just opening the door for them to behave a new way with you. When I was thinking about purchasing a green-broke 7-year-old Arabian, he had major bridling issues that would have been a deal-breaker. He got super stressed every time they even reached for his poll and would shoot his head up in the hair to avoid them putting the bridle on. After they spent a week trying to fix the problem, I told them to stop working with him on it and let me try. I successfully taught him the concept of clicker training, to lower his head when presenting the bridle (helping him to relax and focus on me), and then to accept the bridle without issue. Though this is the only thing I ever worked with him on clicker training, every time the problem reappeared, I simply brought out the clicker and the bridle was on in a few minutes, so he clearly remembered and understood the concept. I chose not to clicker train him beyond that because it was just easier to work through the system we had, but thinking back, I might have gotten along with him a lot better if I'd kept it up (he had a very worried and stressed personality that took his attention everywhere and he rarely relaxed and focused on his job).