This is kinda off topic, but horses should drink more in the winter due to the fact that they lose a lot of moisture from their body while breathing(hence the vapor coming from their nose when breathing). They may not drink enough because the cold water hurts teeth or is uncomfortable in some sort of way. Like was said before, providing either warm water or a heated bucket will greatly increase water intake.
Also, to add to my post about soaking alfalfa cubes, they also make alfalfa pellets. They are just like the pellets in feed, and I know my horses will eat them better before cubes.