Eeek, there are a few more experienced folk on here than me so I'll just bump this thread by giving my view of it and why and when I use clicker. Hopefully some more knowledgeable peeps will add their wisdom.
I was an inexperienced horse owner (and still am lol!) who didn't really bond with my horse. He's not totally driven by his stomach but he is an energy saver so I need to find a good incentive to get him to do things. Most of the time he wants an easy quiet and pain free life....don't we all!
We had/have a few issues - mounting being the prime example but also him being spooky and unconfident, unresponsive to my groundwork, etc.
I explored some nh type stuff and would now say I pick and choose and do what I want with that but the clicker is incorporated into what I want to achieve. A mix and match sort of approach. What I'm saying is that I'm not totally clicker dependent but I think it's taught me more about timing and thus I've now been able to use approach and retreat, pressure and release, all more successfully than before.
If you're psychological at all, clicker is reliant upon operant conditioning. Achieving a desired response by shaping existing behaviour with positive reinforcement. Basically taking the basic building blocks a horse presents us with, and just encouraging them little by little in the right direction of what we want them to do by reward.
Before you start anything you should really have a read of any book by Alexandra Kurland, or there's a few websites which explain more. The first thing the horse needs to learn is the link between a behaviour, the click and then the treat. The click, when given in a timely fashion, develops as a clear signal to the horse that he has done a good thing, and that is then rewarded with a treat. Using a simple target, getting them to touch it with their nose by placing it in close proximity where they are liable to try to touch it, is a good place to start. Then move it around once he gets the link.
The mugging thing can actually be trained out of them - you simply have to encourage them to turn their head away, click and then reward. (simply, but a mistake I made was not to train this very well! My horse didn't really mug me as such, but he does look to me for the treat and wasn't really paying attention to the task at hand. Ive had to go back a step or two to retrain this and I'm still working on it :redface
I think it can be good for horses as they realise they can exert some perceived control over their situation and they show an active interest. It gets their brains working. I don't use it for everything, but can see its advantages.
Sorry for the wittering, hope this helps!