I'm also of the opinion of giving notice for something like that. I would want/expect notice and would be irked if someone strange just showed up and went out to my barn. That said, I'm a private barn and only have 2 boarders, might be different at a big barn that is exclusively a boarding barn. I see too much risk with someone unknown coming in. How is the BO to know who that person is and what their intentions are unless told by the owner? I wouldn't want someone feeding anything to any horse without knowing it was okay. What might be fine for the horse they came to see might not be okay for mine or someone else's that they chose to feed too just because they were there. Not to mention the liability, if no waiver is signed many insurance companies won't cover and where does that leave the BO? Not to mention things like carrying in a communicable disease from another barn, how would one know if said stranger hadn't been at a barn with a strangles outbreak or, or, or.
Our barn was cleaned out in the mid 90s (tack room & lockers were emptied) - culprit, friend of a person that had came to buy a horse from my grandfather. Thankfully insurance covered the almost 20k worth of stuff that was stolen but goes to show you can't trust people even if they seem to have good intentions on the surface.
Aside from the liability & risk, I would think it common courtesy. If I were the boarder, I'd want to let the BO know for the same reasons I'd like to know as the BO. I would expect a BO to be leery of a stranger they'd never met stopping and saying 'hey, going out to feed one of the horses some crackers" if they'd not been notified that would be taking place. It takes all of a minute to text or make a quick call.
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.