Bevendre

As far as I know, Applejack says that she won her hat at the fair, but not how she won it or from whom.  As such it is still possible that the hat is her fathers.
As for how I feel about it, I think it very likely and touching.  Applejack has been shown to be very attached to her hat, refusing to relinquish it when dressed formally.  This is distinctive of an emotional attachment, one that could very easily stem from memories of a lost loved one.  As has been shown in the Apple Family Reunion, and said by Faust, Applejack’s parents are dead, and this would establish such an intense attachment in Applejack to her hat.