The scheduled opening of the ski season is the start of December, although if the snow allows they open earlier. Sometimes they can't open then, although generally they're able to produce artificial snow if necessary. I'd be pretty confident that some of the resort will be open by Christmas, but probably not all of the runs. There are a few other disadvantages of going around Christmas: the resort can be very busy, the days are relatively short and it tends to be quite cold.
From Granada it takes around 30-45 minutes to drive up to the resort, although it can take quite a lot longer if the traffic is bad. Costa del Sol to Granada depends on where you are staying, but probably close to 2 hours.
One of the big hotels is the Melia, which I think has a spa, but quite a few of the hotels have spas and other facilities to cater for non-skiers.