Well as other OP mentioned it depends on your interests, I mean December/ January is a wet month in Jordan. so Canyons will be closed, hikes can be organised but weather is so fickle you cant really plan anything! Aqaba would be nice, weather is decent however, water is too cold to swim, a dive might be good if interested. Wadi Rum would be freezing as all deserts in the Winter, the joy of it is at night, when they light a bonfire and mingle with other tourists (I might be mistaken but that's purely subjective!).
The dead sea is quite nice that time of the year, went there so many times during winter, temp usually varies but stayes in the 20s. might get a bit chilly
since it is winter and as any other country, activities are usually limited, (As suggested by fellow travellers) why not combine Egypt and other regions, to your travels. Sharm El Sheikh would have nice, mild weather.
Not sure If I answered your question, but hope this helps
Happy travelling