Something You Don’t See Often; Alan Jackson Without a Hat to Honor George Jones
I once heard a rumor, he was asked to perform without his hat at a church and he told his manager to cancel the show. Now, I don't know if that's true, but they say there's some truth to any rumor.
Alan even wears his hat while water skiing in his 'Chattahoochee' video.
There is a few shots of Alan hatless. This is one from 2005 at the CMA Awards in New York City.
This one I found on Taste of Country.
I also found a website with a gallery of really old pictures of Alan without his hat. There's even a few without his signature mustache.
It's a rare occasion for Alan to remove his hat in public, but it seems it's only done at monumental moments.