If heading to jaisalmer, book the desert camp in advance for a bargain. Mika rai is the one I stayed at. It costed me 600/- per person with food and no stay.
It does get quite chilly at nights in december.
I had gone to Udaipur last year around the same time. For a three day trip, I guess Udaipur can offer you more. Jaisalmer doesn't offer much though the stay at desert camp is good fun