Tips for a Marrakech to Fes desert tour in January?

I'm finally booking my trip for January and I've settled on doing a one-way trip that includes the desert, mainly because I don't want to waste time going back to where I started. I've been looking at a Marrakech to Fes desert tour 5 days itinerary that goes through Ait Ben Haddou, the Dades Valley, and Merzouga, which seems like the classic route everyone recommends. My main concern is the weather though. For anyone who's done this during the winter, how cold does it actually get in the desert at night? I'm trying to figure out if my regular winter coat will be enough or if I need to pack something heavier. Also, are any of the mountain passes ever an issue in January? Just want to be prepared and not completely freeze during that camel ride!