In other editions, the rules for disarming an opponent are clear. In 5, not so much.
There's an optional rule:
The optional rule for disarming (DMG p271) is as follows:
A creature can use a weapon attack to knock a weapon or another item from a target's grasp. The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.The attacker has disadvantage on its attack roll if the target is holding the item with two or more hands. The target has advantage on its ability check if it is larger than the attacking creature, or disadvantage if it is smaller.
But since it's assumed in 5e that picking up an object can be part of a creature's movement during its turn and can pick up before an attack, disarming becomes pretty pointless.
Since disarming is classed as an attack (this is specific to something in the opponent's hand) it is not allowed as part of Mage Hand. Same applies to pushing someone.
Taking arrows out of an opponent's quiver would actually NOT be an attack technically, as it doesn't take it directly out of their hand.
You can use the hand to manipulate an object, open an unlocked door or container, stow or retrieve an item from an open container, or pour the contents out of a vial.
A quiver definitely qualifies as an open container.
Do keep in mind several things:
- The hand is not invisible. (Unless you're an arcane trickster)
- It can never be more than 30 feet away.
- This is a cantrip and it is not sneaky. It can't be used to properly pickpocket another creature without them noticing (again you need to be an arcane trickster for that). However, it can cause them to try and prevent the object being taken, which would be an action, if they have already used that up--although, once they have it in hand, there's no grapple check, they would automatically win.
Here's the rules on interacting with an object--this applies to the person who is retrieving the object (NOT TO MAGE HAND). As you can see, it's a free action to pick up or take the object that's been taken by Mage Hand. But, at least, it uses up their free action.
The PHB (page 190)
You can also interact with one object or feature of the environment
for free, during either your move or your action. For example [...]
you could draw your weapon as part of the same action you use to
attack. If you want to interact with a second object, you need to use
your action. Some magic items and other special objects always require
an action to use, as stated in their descriptions.
Although Arcane Trickster specifically mentions this as a special ability concerning mage hand, implying that it would not be allowed otherwise:
You can retrieve an object in a container worn or carried by another creature.
I would argue that an OPEN container, such as quiver that is easily accessible--not anything like a pouch or anything secured in any way (even a sword would be difficult) should be allowed.
Allowing it to be tried doesn't mean it will be successful. Since there is no check, if they notice it (and they will because it's obvious) they can prevent you from taking an arrow. (Keep in mind as well that it would be ONE arrow at a time). This, combined with the fact that it's a free action for the person picking up the arrow, means that the only thing you'd be doing gameplaywise is taking up a free action. You can try, but it's pretty likely that you won't be successful except as a distraction.