As a point of clarification for this post, I'm just trying to figure out if it's actually possible to take an enemy's item directly from them during combat, all in the scope of one turn. Since Disarm doesn't technically allow you to directly steal an item (it falls to the ground and opportunity attacks also seem debatable), is there an action or feature that allows you just take an enemy's wielded item and put it in your hand in one fell swoop?
Contest rules should cover that(p. 174 PHB), but your DM will most likely give you disadvantage1 if you try this in combat and no other factors are involved. Your DM will decide on a Strength based ability check (Athletics, most likely) or Dexterity based ability check(Acrobatics).
This contest means that you use your action to attempt that grab, opposed by the enemy's ability check. Your bonuses apply to your die roll, the opponents' bonus apply to theirs. (The optional rule calls for your opponent to drop the weapon, not for you to grab it and have it under your control, see below).
Should the DM impose disadvantage? That's a judgment call, but it makes sense. While some situations like surprise might lead a DM to give you a straight up attempt with an ability check, it would most often require an ally to use the Help action (offering advantage)(PHB p. 192) to have your advantage cancel out the disadvantage.
1 Why should your DM give you disadvantage for trying to grab/snatch the weapon?
The Disarm rule is an Optional Rule under Action Options that makes it a Strength or Dexterity check made at disadvantage (DMG p. 271) if the weapon is held in two hands. The optional rule gives advantage if the attempt to knock a weapon from someone's grasp is a larger size than the target, but disadvantage when the disarmer is a smaller size than the target.
But that is using a weapon to knock a weapon from another's grasp.
Grabbing it would be more difficult.
What's good for the goose ... how easy do you want it to be for the NPC's or monsters to grab your sword?