There are MANY carts/kiosks in Epcot that are cash only. I know this because we went there without any cash one day - zero, zippo, not one dollar, and there were several places where we couldn't purchase anything. It was very frustrating. I would guess that the other parks are like this as well. I don't know this for sure, because we never made that mistake again, and I don't recall how we paid for things in the other parks....
To be on the safe side, I would always bring SOME cash. I think all CS places accept other forms of payment, but snack carts and kiosks are iffy.