Granada is an amazing place. To quote Garcia Lorca, "Granada smells of mystery, of something that cannot be, but nonetheless is". I lived there nine months during university, did some climbing but mostly partied... Anyway, I think best option would be spring. Winter is nice and warm but I got a very rainy one... Big multi pitch can be found at Los Vados, but there were short multipitch routes (3/4 pitches also at Los Cahorros, a nice crag just half an hour from town, close to Monachil village. It's a canyon that goes on forever. Lots of sport climbing on hystorical routes, home of some of the first 8's of Spain and infamous for grading (7b=8a). Now there's also a climbing wall somewhere close to town, can't remember exactly, La Zubia perhaps. Don't know much about snow and long hikes, but we once did a two days trek that was nice! I know more about bars and drugs to be honest... Oh well, just 23 years ago.
Andalucia sport climbing by David Munilla. Needlesports suggest a new edition is out in January 2017. Online topos to some small local crags here.March should be a good time to visit.
El Torcal is a cool place to visit even for a non climber, it's like a larger-scale limestone Brimham.
My better half and I went there in Feb - we had a week staying on the south coast with some day trips to Grenada and the hills and the weather was glorious. Sunbathing was just about do-able on the Costa and perfect temps for enjoying the Alhambra, which is a total must-see, some of the best architecture I've ever seen. We also went to the Alpujarras which was wonderful. Rolling hills and lots of small villages with flat roofed white-washed houses. Felt more like N Africa than Europe, and should give a good day or two's walking.