When Annie storms out of Bella's house she isn't wearing her hat, and she doesn't have it on when we see her riding away either, but when she marches back in, she has it hanging on her back.
We see Annie ride through a torrential downpour, but then the weather clears up. When she stops at the fork in the road, her hat is perfectly dry, but a bit later when she arrives at Bella's cabin there are water drops on the hat.