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At the beginning of each player's draw step, if Howling Mine is untapped, that player draws an additional card.
First, there is no bent arrow tap symbol, so how would it tap to begin with? The activated ability is dependent upon being untapped, so tapping it would just prevent activation?
Second, what one-drop could I use to make this work to untap for me, but tap to prevent everyone else from benefiting? If I had 4 cycles in play, that could mean 5 cards per turn?
In the first release of the game there were 3 different types of artifacts: Poly, Mono, and Continuous. Poly Artifacts were artifacts that had activated abilities that could be used without tapping the artifact. Mono Artifacts were artifacts that required tapping to activate their activated ability. And Continuous Artifacts don't have activated abilities, however their abilities stop working when they are tapped.
Howling Mine was printed in Alpha as a Continuous Artifact, so its static ability didn't have an effect if it was tapped. The rules worked like this until 6th Edition, and at that time the rule was mostly just dropped, except for a few cards that received errata to maintain that functionality. Howling Mine was one of those cards, but there were a few others like Winter Orb.
One-drops that can be repeatedly used to tap them would include Trickster Mage and Vedalken Certarch. And yes, you draw one card for each Mine you have on the battlefield, so with 4 Mines you would draw 5 total cards.
Aside: with the right deck, you don't need to worry about your opponent having 4 extra draws / turn. An example of this, is turbo fog.
