by logic alone, a men on horse can do anything a men on foot can do, because a man on horse can dismount whenever he wants. so cavalry should be able to gather any resource infatry gathers.
the choice to limit cavalry to hunting has more sense if you think of them being of higher social status, so they couldn't be bothered farming or gathering berries, but only hunting because that was more common among warriors and aristocracy of all ages.
I think the game is fine now, by this regard.