I wonder if, when you take them somewhere else, whether you are subtly different, more serious, and anxious that they do well for you, just because you are now somewhere else and in 'public' display. And if they are naturally more willing to follow your lead when they are not in their own territory. Bay spooks at things here, but on trail he will trust me to tell him how to handle new things.
My horses and dogs knew the difference between sloppin along and 'show day' before I did anything obviously different. In the case of the horses, they'd find their fire at Arab shows and I'd get much bigger action than I would at home. In the dog's case... he would misbehaved in ways because he knew he couldn't be corrected at shows ;~D
You could very well be correct that it is more me that is differnt and the horses picking up on it.
OUt in public I have a fear of really looking like a fool on my horse:), I'm much more aware of myself and what I'M doing. At home I've caught myself sitting there on the horse flopping around like a sack of shit:)
Becky