From the weather and camping side, the trip is weather dependent - we've spent many days on the water in November and December. If there are no storms expected, the water is unusually calm - glass much of the time, so daytime temps in even the low 50's are t-shirt/shorts weather if it is calm and the sun is out. And many days are even warmer. We've spent several Thanksgivings on the water, actually eating outside under the sun, as well as our annual Christmas to New Year's Day trip.
But winter storms are ugly, technically no worse than summer, but from a safety perspective I treat them much differently as 1) there is no one on the water to help you if you run into problems (including NPS), and 2) the water is cold enough that hypothermia would set in quickly if you were in it for very long. I personally treat boating that time of year as I would if I were on the ocean, pretty much planning on being able to save myself and crew and try not to depend on needing anyone else unless a major unforeseen emergency occurred. It's really mostly a mental change, and not taking any chances - if in question, don't do it whatever it is. Always wear life jackets, have an emergency pack, etc.
I will add that we've experienced snowstorms on the water the past couple of years, including over 8" last holiday season. They are even fun as long as you are dressed correctly and can get out of the cold when you need to.
Lastly, luckily, nobody on WW listens to me on how nice it is to boat Lake Powell in the winter months, so you literally may be the only boat on the water! It's awesome, calming, quiet, and kinda creepy all at the same time.
BTW - I have actually done some fishing during Nov/Dec also and have done pretty good catching SMB and crappie (for me anyway). But I'm sure others with more fishing experience can chime in on that question of yours. -Doug