I understand what you mean. I would urge you to remember this: there is no reason to constantly pressure an opponent with Johnny Cage. As a matter of fact, Cage doesn't really play that way in this game. If this were MK9, or even MKX, then he would be. He is a post-sweep distance character that makes opponents whiff and then hit opponents with F3/F4/B3 for their troubles.What I'm having trouble with is to not be stupid in this match. I mean, since his projectile wins the trade into full combo and he can check you with slide, and even add the trap once in a while. And then you have those f2 into the special cancelable amplified which gives pushback and is safe and on top a low starter which is also safe. It's hard to remain patient and play defensively, and enables him to be lame and you having to chase and be keep pressure whenever close. Avalanche can play completely safe minus the slides, and that puts you in a strategically inferior position.
Instead, you need to obtain a life-lead and then back away and let the Sub come to you. That's when you can start checking them with surprise fireballs from mid-screen and closer. That's when you begin using F4 into EX-forceballs into more pressure. I forgot to mention that EX-Forceball pressure absolutely works on Sub-Zero, so you need to be taking advantage of that.
Actually, if you don't mind, could you post some of your match footage against a Sub-Zero? I play both characters as my main, so I can definitely be of help to you.