Rockman
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My interpretation of a sharp horse is one that is quick off the leg, that responds to a small nudge, rather than a kick. I'd envisage a quick thinker (although not necessarily rational in that quick thinking) and quite on their toes when ridden out hacking and perhaps one that gets a bit stroppy/fizzy when being asked to do something new that it doesn't understand.
You just described my horse to the letter!
I class sharp as exactly this and from experience it is mostly irrational thinking. Very hard to deal with as the horse is often unforgiving towards the rider and very opinionated.