It will be mild, but not sunbathing weather. Also be prepared to wrap up warm at night.
It's a great time of year for long walks and going places and seeing things you wouldn't be inclined to in the fierce heat of summer.
The places with all-year-round populations, like Fuengirola, Torremolinos and Malaga itself will have things going on and a bit of life in the bars and restaurants at nite.
It's actually very interesting seeing the change in those areas from summer to winter. They take on a whole new look and feel, especially the bars and restaurants, which can be very cosy, with everything going on indoors. It gets dark early, too. As long as you don't go expecting to be on a sun lounger from dawn to dusk, you can have a very good time. Last winter, some people might remember, there was an ill wind from Russia that blew in freakish low temperatures and the worst chill I've felt on the Costa but, by and large, New Year is a very pleasant time to be out there. I like it.