Deer are individuals and some will scrape into February in my area. Late scrapes may not be productive to hunt, but have seen fresh scrapes in snow during January and early February.
Depends upon the area's herd structure, but as long as does (such as button does) are coming into estrus, there'll likely be rutting activity. May not be peak rut, but breeding continues throughout the winter in some areas.
Watched and filmed a big midwestern buck breed a doe on November 30th a few years ago. Most of the whole day laying and breeding with her all while keeping a couple basketracks at bay.