Of course, there are all sorts of winter climbs. Are we speaking of the High Sierra, or maybe the Desert? If we're talking about the former, you will mostly likely need snowshoes or skis. With deep fresh powder, this is the only practical way to get somewhere, much faster than what one might expect to be about a quarter mile an hour, postholing. Hundreds of books describe how to do this.
There's a few books on desert hiking, where in midwinter, one might think they were hiking in summer at a higher elevation. I've been sauntering along in a T-shirt in Arizona during the holidays.
Then there are the Coast Range and the Great Basin. Both can get snow, although usually not enough to merit special snow gear. It can still get pretty cold, so plenty of the right kind of clothing will assist tremendously.
You can hike in the rain, which most hikers will forgo. I see few or no books on how to do this, so I'll make a few suggestions. Use breathable, water-resistant outerwear, if you can afford it. Underneath use polyester fabrics, for quick drying and warmth. No cotton, or even wool (gets heavy while damp). Have a quick change of clothes in your car, getting back from your hike. Nothing like driving home in wet clothes to give you a cold or the flu!
If there is no big wind, you might try using an umbrella. Remarkable how such simple measures can keep you absolutely dry.
There's plenty more you will learn, or find out, but as I don't know what areas you'll be hiking, I'll save it till we all know!
