I have seen deer drop their antlers as early as Christmas, but that was a deer that had been stressed by being wounded. Antlers drop off due to a change in the levels of hormones produced by the pituitary gland. This is triggered by photoperiodism (shorter daylight hours). When the pedicel demineralizes, the antlers fall off. It's rare for them to fall in January but a few do every year. They start dropping in bigger numbers in February, but in March most of them shed. If I had to guess, I'd say that 60-80% fall from the last of February to the middle of March here in Northern Iowa.
From just before Christmas to January 10th is some of my favorite time of the year to hunt here. We usually have a lot of snow, and the deer are all bunched up around the available food sources. It's easy to look over the herds and pick out the one you wnat. Not quite so easy to get him, but it is an enjoyable time to hunt because they are more predictable than at any other time of the year.