Why is my AWD light coming on (solid) in cold weather only?

Probably a wiring issue in that system, law of expansion and contraction, start with connectors, if nothing there then onto grounds and main wiring. Your going to need a wiring diagram of the entire circuits.

Maybe the programming think you should be locked in AWD when it is below freezing because of possible icing of the roads. Call a Honda dealer and ask someone in service.

Cold weather plays havoc with car electrical devices and cars respond in weird ways. One of those is to turn on random dash lights. The colder it is outside, the harder it is for electricity to flow properly. As your problem occurs just below freezing, I'd say that the battery is week, and further weakened by the cold. Or the battery connections are loose or corroded and resist current flow. Otherwise, it might be that you have a sensor in the AWD system that's icing up or is going out.