There’s a lot of research (old learning & behavior stuff) demonstrating that intermittent reinforcement produces more robust behavior than continuous reinforcement (e.g., slot machines… they don’t reward every lever pull, only some lever pulls, and that uncertainty is part of why they are so addictive). So if you want robust behavior, it’s actually better to not treat every time the horse does xyz (to say nothing of the fact that then the first time you don’t treat, it can send them into a tail spin
). So, click for all good/wanted behaviors, but don’t treat for every single one - treat occasionally (use your judgement). (Full disclosure: I never quite believed that intermittent reinforcement produces more robust behavior than continuous as a blanket rule, but lots of old white men did lots of old experiments in the 50s, 60s, and 70s to demonstrate this. Personally, I think it’s probably more situation dependent than they’d like to admit, but who am I to argue with the literature?)
And as someone mentioned above, the beauty of clicker training is that the click becomes the reinforcer itself, independent of the treat. So yes, you can absolutely use clicker training under saddle because not every click means stop and get a treat. I’ve used it to great effect training my horse through FEI - I click with my tongue for a nice change, nice pirouette, nice half steps, etc. I’m not sure how other riders feel about me clicking away in the arena but they’ve never commented so
But I am often vocalizing to give my horse guidance, whether its with a click or my voice so perhaps it all gets drowned out.
(Side note, I definitely do not do only R+ - I use a lot of R- also, because as someone mentioned above, it’s really hard to do any meaningful work with just R+. And frankly, I think R- is a perfectly good tool when used reasonably - horses use it with each other all the time, so why can’t I? The trick is to set up a learning/teaching environment where your horse knows a little pressure just means “you can safely keep trying answers and I’ll let you know when you try the right one”).