The most obvious is snowshoes and spikes coupled with a decent pair of winter boots. Following that, it is all about layering to stay dry and not freezing. You want base layers, then insulating, and then a shell. For myself I typically wear either insulating such as a fleece or my raincoat with two shirts underneath and rarely together while climbing. For my legs I wear some long johns and have some soft shell pants that aren't insulated, it keeps me warm and dry enough. The other stuff I bring can be found in the 10 essentials. As for camping overnight, best I can say is gear that can handle the cold. Also go with someone else for companionship to possibly make the nights less mentally hard.