'hauling', is a special case of being able to carry something.
i'd wager that even creatures without [GRASP]ers should be able to haul stuff around.
hunters for example might have bolts in one hand, crossbow in the other, and still haul corpses around just fine.
pulling out an embedded weapon(such as a bolt) is another thing altogether i think. i would think that it counts as an equipped item than you remove.
and rather than it appearing in your hand, it is dropped even though a hand should be required for the action in the first place.
toady still doesn't have this under very good control, as can be attested to the infamous wearing of the 100 shields in adventure mode.
in general i think that the control for wearing items and armor is just temporary patchworks without a true and common design background. dwarves in fortress mode for example are very reluctant to put on gear up to their limit like they are able in adventure mode.
heck, if you get a peasant in fortress mode to put on a boot for hunting etc., then he will drop either one sock or a shoe to accomodate the new item(there are restrictions for wearing items).
however, upon losing said piece of armor, he will walk around for the rest of the game with either just a sock or just a shoe, even though they should be able to wear both - and do indeed start with both by default, which can never be worn at once from then on.
i think toady is reconsidering the layer system of armor, which enables dwarves to wear 3 chain mails and one plate mail, if there is not more practical concerns behind this, such as pathfinding slowdowns or the like.
also about removing armors. in fortress mode whenever a dwarf wants to put on a new item, it automatically drops at his feet the old armor in the same turn. the mechanisms for removing stuck bolts could be different for the two game modes, and does not seem to need or make use of hands in fortress mode.