Spain's a very unique country, weather-wise. Much of the answer depends on where exactly you'll be in the country. Big cities like Barcelona and Madrid are fairly temperate with highs in the mid-upper 50's in December. Though Barcelona is on the coast, so the temperatures are a bit more maritime than Madrid (located in the middle of the country), and snowfall in Barcelona is not common (it does snow in Madrid). Where abouts in the country will you be?
As for what to do, I've only been to Barcelona, and I enjoyed the Gaudi-designed
Guell Park, and the
Sagrada Familia cathedral (also designed by Gaudi). La Rambla is also great for experiencing the citylife as well as finding great food and drink.