Yes, clicker training *done properly* definitely works well on any animal(even husbands & kids!!), as it's basic behavioural psychology in action. I find it is especially great for teaching 'good' manners to 'rude' or 'aggressive' horses quickly & effectively. It is a method of training that teaches the animal to *want* to do what you ask & try for you. It is also a fantastic way of teaching yourself to be a better trainer, as it gets you focussed on your timing, focussed on all the Good Stuff the horse gives you & what you can give to the horse, as well as being consistent & teaching new behaviours in small increments, which is an important teaching principle.
I think what is most important to focus on is understanding the *principles* of it, rather than getting hung up on the specifics - eg plastic clicker, food treats, etc. Those are useful 'tools' but are not necessary. Any short, sharp, unique sound will work as a 'bridging signal' and a positive reinforcement doesn't have to be(& sometimes isn't) food treats. It is anything that that horse at that time truly desires, so will work to earn.
Likewise while many people blame food for their horse's bad behaviour, it's not the food that causes this, it's the *behaviour* that has been inadvertently reinforced with the food that's the problem. Eg. A horse does something 'good' but when the handler gives him a treat, he has his ears back or snatches at it with his teeth. If the reinforcement is given(be it food, release of pressure or otherwise) then, the horse has effectively *been taught* to be 'pushy' or 'mouthy', because that is the behaviour that has worked for him. It's not the food, it's being aware of what we're teaching that's the issue. People aren't very good at positively reinforcing horses in other ways and food is often the only effective reward they ever get, so they don't realise the difference is that it is just a more powerful & therefore effective teacher than other methods.