I always check for hairs on the rub, especially if I think it is a new one. Down here, Elk continue to rub throughout the winter, especially on Sitka Spruce if it is available. Other conifer get beat up too. The DNR biologist explained it that the groups of raghorns are like a bunch of teenage boys, just breaking stuff 'cause it's fun. One hair found caught in the bark paints a better picture of the culprit responsible for the rub.
Statistically, I think the books say that 99% of does have been bred by mid-December, and something like 99.9% of the does are bred by the end of December. That leaves one doe out of a thousand still going through estrous cycles by the start of the new year. I'm guessing that single buck may still be making or freshening rubs at this time, but probably not too much later than that.