Ice Climbing is the logical pastime for a rock climber seeking that reeling feeling in the winter. Its climbing up frozen water falls and rock faces in the winter months, think of the views, the excursion, the feeling that you will get. Fancy giving it a try?
Ice climbing takes place below freezing, sometimes well below. Dress accordingly. In more temperate areas it is Ok to get cold and wet while in colder areas getting cold and wet can have fatal consequences.
Take many pairs of gloves. You will get them wet and then you'll freeze if you don't have any dry ones. A baclava really helps on those days when it's cold and the wind is cranking.
Take some sort of puffy coat (preferably synthetic, down will do) for while you're standing around. If you're "ice cragging", it'll be a stop and go activity and you'll want the coat for belaying.
Dress heavy on the legs, once you're in thigh deep snow or have boots on forget trying to add layers to your bottom. Adjust for conditions with your upper body clothing. If you don't have any waterproof clothes, I'd take your own car to the crag. That way when you get wet you can go home when you start freezing too badly.
Take a thermos of hot tea and lots of food. It'll make you feel better to have something warm to drink and eat, as well as make you popular with folks who didn't bring any of this stuff.
I don't know if you rock climb with a helmet, but you'll want one for ice. Lots of ice will fall, and if a tool rips out you'll want your helmet to stop it, not your scalp. If you have "cold" hands or feet, get those chemical hand/foot warmers for cold days.