I actually spoke to Steve Averill, of Four5One about this when I met him in Cleveland at the R&R Hall of Fame.
I said: "Seems that Edge was fine with no hats for all the Pop promo pics and video snippets; even the toru launch at K-Mart. But by the tour, it was back to cowboy hats and then beanies since".
Steve said: "We've all told him he looks fine without the hats. But he feels more comfortable with them".
But I agree. I think he looks fine without the hats. I think of it the same way I do about Bono's hair. Some like short and some longer... he's the same Bono either way. Same with The Edge - hat or no hat, he's still our guitar hero! But if he feels comfortable with hats, I am good with that.