I spent last Christmas in Malta and it was definitely cool, and rained a lot.
But apparently we were just unlucky. We stayed in St.Julian's Bay. There were plenty of bars, restaurants etc. open, and no shortage of places to shop etc. In fact, the only thing we found closed was the outdoor pool at the hotel.
Having never been to Malta before, I was surprised at what a busy, bustling place it is. We caught buses all over the place and everywhere seemed to be the same. I hope you have a great time. Take a cardigan and a mac though!