Some of them are open nights (and weekends), yes. Not all, but a lot of them are. And some of the ones from the "new school" like the Wafels & Dinges truck, etc. move around and have a different evening location than daytime (follow them on Twitter to keep up).
The most famous example of a "night time" cart is the halal cart at 53rd and 6th. The famous one on the southwest corner would only open at sundown and stay open late, until 4am, IIRC. (They later added another cart that parks on the southeast corner during the day).
A related thread here, on Midtown lunch: