You should eat something, but you should first make sure that you’re really hungry.
I personally find that late night is when I most often confuse hunger and thirst. Before I go diving into the refrigerator, I’ll drink a glass of water to make sure I’m not just dehydrated. You might want to try the same.
If you find you’re still hungry, eat. Just keep it light. You’ll want your “snack” small enough so that you can barely feel it in your belly when you lie back down. Maybe try a little fruit, a really small bowl of cereal, or a couple of bites of leftovers.
Remember that all you are looking for is something that makes you no longer hungry. You have to fuel yourself with a little something to keep your body humming along efficiently, but you don’t want to load yourself up with extra energy that has nowhere to go but your thighs either.
Ice cream never sounds better than it does at 2am, for sure. At the same time, eating lots of high-calorie (high-energy) food before going to bed is one of the secrets behind building a world-class sumo wrestling physique. You can decide what you’re looking for and respond accordingly.