I strongly disagree with Pete.
Cruise when you want but choose the cruiseline/ship to match your expectations. I have taken a number of cruises over Christmas/New Years on Regent; a luxury cruise line. I have found a number of teenagers/early 20s on the ship traveling with their folks. In fact, I seek out these youngsters for my trivia team each time; they have a wealth of knowledge that I don't have.
There have been some kids but not many. It is definitely an adult atmosphere yet your kids will find lots to do. The max passengers on a Regent ship is 700; there are not that many cabins that can hold three or more so not many kids.
This allows you to choose the time of year convenient for you and your kids yet allows you the experience you want.