If nothing else, putting the clone on the screen, even against a player comfortable with dash blocking to eliminate it, limits that opponent's options to a degree and takes up his mental resources, which Sub Zero can exploit very well.
If you run into an opponent that takes even a split second to decide what tactic to use against the ice clone, then you have got him all day. There are quite a few options. If the opponent is the dash block type that likes to destroy clones, catch him with an enhanced ground freeze. Unblockable, and that leads into some really frostified combos. You have the slide because dash blocking is a high block especially if you leave that clone in the air. Catch the opponent with the slide, get in close and pull off a good combo.
Of course, these aren't the safest (especially the ground freeze; landing that beast is dominate), but you can force opponents to get pretty predictable with Sub. See how they react when you send freezes, clones, slides and ground freezes their way. Typically you can immediately determine how they will react and adjust accordingly. Obviously, the more advanced the opponent is, the tougher it will be to predict, but with this icy beast, one opening can do it for you.
Another way to get out of that zoning concept is to become an aggressive Zero. Come out hunting with this guy. You don't have to wait until the opponent makes a mistake,
force him to make the mistake. I know this is unorthodox for the typical Zero player, but getting more offensive with this character puts him in the top tier. I wish I knew how to be more complete on offense as I would dominate most opponents. To me, Sub-Zero has the best defensive package on the game. Couple that with a punishing offensive attack with quick counters and persistent, relentless combo play (and always good blocking) this character is above and beyond the definition of a beast. Clone as a counter instead of blocking and work the slide when you are certain it will hit. I think most Subs overuse the specials. Yes, it builds the meter, but getting up close and personal is highly effective with this character in my opinion. I don't see zoning as a first option simply because his freezes can be punished because of their slow throw and charge rates.
Look at the speed in which Brady plays this guy. He comes out like a beast and it is effective, and to me, this is the appropriate way to play. Obviously this guy is probably the best with Zero, so he makes it look easy, but I would suggest to stop backing up so much and bring the pain. Sub-Zero 24/7/365.