This is some stuff I have been thinking regarding ZSS.
1) Suit Pieces have to go!
I've been thinking to tackle ZSS by not using grenades at the start of the match until all suit pieces have been eliminated from the stage. This means making it a priority to get rid of all suit pieces on the stage. Snake lacks really any mobility and good follow-ups from hitting ZSS with a suit piece. On the other hand, suit pieces put Snake into the air where ZSS can wreck Snake. Pulling nades has periods where you cannot defend yourself at all.
So, staying near the ledge would seem a decent location to be at. If you spot dodge a suit-piece toss, it goes over the ledge. And really, ZSS can't do much with a suit piece in hand. She can throw it or use specials. If she does a complicated button input you can use other options upon picking it up such as charging a fsmash and other gimmicky things.
2) Don't be wasteful of your movements
Snake gets juggled well. ZSS can keep a juggle going. You need to make sure you don't make a hasty movement that will get you into trouble. If your rolling, shielding, spot dodging, or air dodging out of fear it will come around to bite you in the butt. Same thing with nade reversals to get out. Once used, your vulnerable for a period of time. Oh, and same thing again too for your attacks.