You know, I think I saw a comic where Applejack's dad was telling her "One day this will be yours." while holding his hat and pointing to the orchard. The joke was that he was referring to the hat.
I actually kind of like the idea of AJ's hat being from her father. That is to say, I kind of like the idea of it as a keepsake for AJ to remember her dad by. Hell, I'm sure a touching fanfiction could be written or a small fancomic could be made from the idea.