A long time ago I started to do bits of clicker training with Pinto. We didn't do much though, and it never really progressed ouside of his box.
However even after about 3 or 4 years after I last did any training if I walk to his box and put my hand in my pocket Pinto will back up, if he doesn't get a treat, he will back up again... then turn his head away, then pick each of his front feet up in turn, then dip his head, bless him.
Although I no longer "click", if he goes through his repetoir, I'll ask for something specific, then praise and give a treat (rather than treating for going through his moves).
Has anyone else found that thier horse will spontaneously "ask" for a treat long after training has taken place?
Sorry to take so long to respond...this is such a busy time of year...in a good way though!

So YES is my experience!! I did a wee bit of work with a mare and just got her started on taking her head back away from the treats so kind of posing a little but that was all (she wasn't my horse - actually she was a brood mare that didn't get much handling so I was just fooling around more for my own fun than hers).
Well...I was visiting the farm where she lived about 3 years later and was talking to the other horse's at the fence sort of just in passing (the lived in a small herd) and I noticed her hanging back a wee bit...maybe 30 feet from the fence and she was POSING!!!!!!!!!!!!!!! Blew me away!!!!!!!!!!! So I jumped in the paddock and ran up to her to give her a treat

It was quite amazing. So she remembered the behaviour and remembered me and I must have been wearing very different clothes and I didn't have a treat bag on or anything...very cool!!!!!!!!!!!!!!
I assume their remembering will be somewhat dependent on the circumstances surrounding the learning experience?? So if they are really calm and relaxed and enjoying the learning, they'll probably learn it better and remember for longer...??
However, it must be Murphy's law because I swear they are very quick to forget behaviours that they DON'T want to do!!! And NEVER forget the behaviours we wish we'd never taught them!!!!!!!!!!

It also has been my experience that some odd behaviours I taught but just happened to teach well (made it clear and simple and my timing was good and the horse really understood etc), they'll seem to hang onto those and offer them more readily. One of those is when I'm working in the barn I clicked Ruby for turning his head slightly away...I was trying to work on just staying quiet with his head and not making faces or biting at the stall walls and doors to get my attention but my click caught his head turning away a little bit. Not such a bad thing but now when I'm pottering around the barn and 'ignoring' him I see out of the corner of my eye him slightly turning his head away. I try to always click now when his head is on quiet and straight and ears forward but about 4 years later he still will try that little head turn away.
So yes...incredible memory's!!!!!!!!!!! Which is why I try like crazy never to let anything bad happen to my horses ever...I know they will never forget!