Seriously NickRiddle is right.
this is easily 6-4 Snake.
Unforunately for ZSS, her biggest weakness is YOUR shield. Her grab is not quick, i dont know the exact frames but its extremely easy to react to. Her forward b (during ground game) should NEVER be a problem. It's extremely slow start up, and can be reacted to with a dash attack which will end the move + damage.
Shes extremely light, kill percent on some stages is as low as 90%. A few reads and an uptilt is all it takes for a stock. Grenades also -can- disrupt her game. Simply put, snake isnt trying to get in, ZSS is trying to get in. Once you realize that her forward b is NOT GOOD IN THIS MATCHUP AT ALL it will require an AGGRESSIVE ZSS to take you down. She can do big damage or gimp once she gets in. But when you learn how to avoid/punish her dash attack and her mixup game you'll be fine.
Take no chances when recovering, go high, be prepared to c4 if it comes to that, mixup your recovery. She can hurt you while your recovering. But if you come back, no matter what percent, she has to get in again to land a kill move. (I once lived to 250+ versus Nick).
Thats all i can think of.
Oh and the only way to deal with Dsmash is to not take chances with it. If you see her starting it up and you ARENT already hitting a button. Just avoid it/shield it.