I know that we were all taught that the Jews during the times of Chanuka played dreidel to hide the fact that they were learning Torah from the authorities. The origin of the minhag to play on Chanuka these days is dubious, but that is one possibiliy.
Nittel nacht, at least from what I know, was a night that Jews kept a low profile because to be seen not celebrating was likely to provoke attacks. People would not kindle any light in their home and in general just go to sleep early (or stay awake davening in the dark and worrying about their families tucked in bed). Nothing to do with cards.
There are plenty of online resources that deal directly with the question of why we play on Chanuka (I just searched) but all seem to agree that there is no concrete “source” for the minhag except that it is practiced. If you want to play for money, you might consider asking a shaila on that. But if you want to play on Chanuka for no money there should be no problem (in my mind; read on for mention of others’).
As I briefly mentioned in my previous post, some are concerned about the “slippery slope” when it comes to playing or learning gambling games. One thing leads to another and poof – one day a person could Ch”V become a real gambler. Everyone has to know themselves and if you think this may be a problem you should take it seriously.
As far as I know, unless one has a tendency to become a gambler the problem is asmachta (what I described above) and if there is no money involved there should be no problem. Some authorities may be more lenient but for leniencies you better ask your own shaila 😉