Yes, it could rain. Then again, you could have delightful weather, much warmer in Marrakech than in Fes, but you must visit Fes. Stay in a proper hotel rather than a riad.

We went on a family self drive two years ago the last two weeks of December and had great weather and a wonderful time. We spent most of the time in short sleeves,capris and cotton pants with a sweater-no rain that I can remember at all? It was always in the high 50's-70's F so we throughly enjoyed the trip being from Chicago!
Please include a trip to Essaouria on the coast for a night or two-beautiful beaches;delightful city right on the water with less expensive souks than Marrakesh or Fez. You will love it!

Bedar, do you recommend a regular hotel because of the heating? Very encouraging responses -- I appreciate it!

We stayed at riads and never felt cold.
However, One tip I would recommend to you is to stay at the IBIS hotel chain-NOT like the ones in France or the UK.These are amazing in Morocco! They have beautiful gardens,pools, BARS!!!(read liquor like beer,wine and cocktails in a Muslim country) and restaurants within each hotel.They are perfect for families as they understand families,provide complimentary breakfasts,etc.
One of the Ibis hotels we stayed at was right on the ocean;another in Meknes was just a 5 minute walk away from the old town area and souks;the one in Rabat was close to a real neighborhood and a train station.We decided after traveling two weeks around Morocco to stay at the Marrakesh Ibis before our flight home and it was not in the old town area but still convenient with onsite parking,close to many things and celebrate New Years Eve in the square!
Maybe because our family is from Chicago but the weather did not need heating in any city we stayed at.

You'll (normally) find that you will be comfortable in shirtsleeves in Marrakech. I'll second the recommendation for the IBIS (the one next to the railway station). It's an easy walk to the main square. In the mountains SE of the city you can expect snow. (I've been caught in a blizzard up there - luckily I was in a 4x4.) Desert camping would be quite cold. Fes might be a bit cooler but it's a must-see.

Days can be sunny & warmish but chilly at night..it could rain especially in cities like Fes Rabat

Maybe I was lucky but I was there a few years ago in early January and I had perfect weather w/o a drop of rain. Nights were cool but very nice.

Well my view of the IBIS by the station is that it is up to at only 2 star in European standards, so maybe not as good as said above in my opinion. The international quarter hotels are all perfectly pleasant and more 3 or 4 star standard