Hi Ya,
Palma can be cold at in December but you can also enjoy some sunshine, the last time we visited in December there was snow on the Mountains and a trip on the Soller train was quite cold but still very pleasant. There is always something to do in the cosmopolitan city of Palma, Shopping, Guided City walks, etc. The cathedral is always open particularly enjoyable around christmas, we enjoy riding on the public buses and visiting some of the resorts that we would not enjoy staying at during the busier times of the year.
Easy jet, Ryanair have flights in December.
Enjoy!!!!!!!!!!
Dave.